Probability & Statistics Past Paper PDF

00072_En_Q25_Əyani_Yekun imtahan testinin sualları Fənn : 00072 Ehtimal nəzəriyyəsi və riyazi statistika The number of ways in which a person can chose one or more of the four electa appliances : T.V, Refrigerator, Washing Machine and a 1. cooler is 43 68...

00072_En_Q25_Əyani_Yekun imtahan testinin sualları Fənn : 00072 Ehtimal nəzəriyyəsi və riyazi statistika The number of ways in which a person can chose one or more of the four electa appliances : T.V, Refrigerator, Washing Machine and a 1. cooler is 43 68 42 56 √ 15 2. A person has 8 friends. The number of ways in which he may invite one or more of thai to a dinner is. 345 435 757 346 √ 255 3. 5 persons are sitting in a round table in such way that Tallest Person is always on the right- side of the shortest person; the number of such arrangements is √ 6 2 4 3 5 4. The number of ways in which the letters of the word MOBILE be arranged so that consonants always occupy the odd places is 87 76 65 43 √ 36 The number of arrangements in which the letters of the word MONDAY be arranged so that the words thus formed begin with M and do 5. not end with N is √ 96 45 76 12 34 There are 10 trains plying between Calcutta and Delhi. The number of ways in which a person can go from Calcutta to Delhi and return 6. by a different train is √ 90 87 14 76 46 7. The total number of 9 digits numbers of different digits is √ 9.(9)! 235 75 79  46 8. In a group of boys the number of arrangement of 4 boys is 12 times the number of arrangements of 2 boys.The number boys in the group is √ 6 4 3 2 5 9. The number of numbers lying between 10 and 1000 can be formed with the digits 2,3,4,0,8,9 is √ 125 457 124 463 346 10. The number of numbers lying between 100 and 1000 can be formed with the digits 1,2,3, 4, 5, 6, 7 is √ 210 457 124 784 523 11. Mr. X and Mr. Y enter into a railway compartment having six vacant seats. The number of ways in which they can occupy the seats is √ 30 23 67 86 63 12. The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs is √ 3024 3568 568 37 658 13. The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is √ 2016 6356 3747 3764 356 14. The number of ways in which the letters of the word DOGMATIC can be arranged is √ 40320 40328 40322 40324 4032 15. 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is 74 97 57 √ 72 78 16. The number of ways in which 7 boys sit in a round -table so that two particular boys may sit together is √ 240 645 234 356 25 17. The number of ways in which 7 girls form a ring is √ 720 6 7 8 63 18. If the letters word 'Daughter' are to be arranged so that vowels occupy the odd places, then number of different words are √ 576 64 23 12 3 19. The number of ways the letters of the word "Triangle" to be arranged so that the word 'angle' will be always present is √ 24 2 3 4 1 20. 4 digit numbers to be formed out of the figures 0, 1, 2, 3, 4 (no digit is repeated) then number of such numbers is √ 96 98 99 94 95 21. The number of 4 digit numbers greater than 5000 can be formed out of the digits 3, 4, 5, 6 and 7 (no. digit is repeated). The number of such is 47 55 26 62 √ 72 22. The sum of all 4 digit number containing the digits 2, 4, 6, 8, without repetitions is √ 133320 1333 133 13 13332 23. If 12 school teams are participating in a quiz contest, then the number of ways the first, second and third positions may be won is √ 1320 1322 1323 1324 1321 24. N articles are arranged in such a way that 2 particular articles never come together. The number of such arrangements is √ (n-2)n-1! n+1 n-1 1 n 25. 10 examination papers are arranged in such a way that the best and worst papers never come together. The number of arrangements is √ 8! 4 5 6 3 26. The number of arrangements of the letters in the word FAILURE, so that vowels are always! coming together is 574 572 √ 576 575 573 27. The number of ways the letters of the word COMPUTER can be rearranged is 40321 40324 √ 40320 4032 40322 28. If n1+n2 P2 = 132, n1-n2P2 = 30 then, N1=9,n2=5 N1=9,n2=7 √ N1=9,n2=3 N1=9,n2=4 N1=9,n2=6 29. If 5Pr= 60, then the value of r is √ 3 5  6 7 4 30. m+nP2 = 56, m-nP2 = 30 then M = 7, n= 3 M = 7, n= 5 √ M = 7, n= 1 M = 7, n= 2 M = 7, n= 4 31. If. nP3: nP2 =3:1, then n is equal to √ 5 3 2 1 4 32. If nP4 = 12 x nP2, then is equal to √ 6 4 3 2 5 33. In nPr =n (n-1) (n-2)........................ (n-r-1), the number of factor is √ R N-1 N+1 N+r N 34. In nPr ,n is always √ A positive integer A fraction None of these 0 An integer 35. 0! is a symbol equal to √ 1 3 4 5 2 36. 7! is equal to √ 5040 5042 5043  5045 5041 jar contains 4 green marbles, 5 red marbles, and 11 white marbles. If one marble is chosen at random, what is the probability that it will 37. NOT be green? √ 4/5 4/7 4/8 4/9 4/6 A jar contains 4 green marbles, 5 red marbles, and 11 white marbles. If one marble is chosen at random, what is the probability that it 38. will be green? √ 1/5 1/7 1/8 1/9 1/6 39. A phone number has 10 digits (0, 1, 2,..., 9). How different phone numbers are there? √ 1x10^10 1x10^11 1x10^12 1x10^13 1x10^9 40. A phone number has 10 digits (0, 1, 2,..., 9). How many phone numbers consist of 10 digits where none of the digits repeat? √ 3,628,800 3,628,8 3,628, 3,628 3,628,80 There are 10 different cereals at the grocery store. 5 of the 10 cereals are made by General Mills. What is the probability of randomly 41. choosing 3 boxes and having none of the three boxes be General Mills? √ 1/12 1/14 1/15 1/16 1/13 There are 10 different cereals at the grocery store. 5 of the 10 cereals are made by General Mills. What is the probability of randomly 42. choosing 3 boxes and having all three be General MIlls brand? √ 1/12 1/14 1/15 1/16 1/13 43. There are 10 different cereals at the grocery store. How many different ways can you choose 3 boxes of cereal (you cannot pick two of the same type)? √ 120 122  123 124 121 At the school cafeteria, 4 boys and 3 girls are forming a lunch line. If the boys must stand in the first two and last two places in line, 44. how many different lines can be formed? 147 √ 144 145 146 148 John needs to pick up his clothes for the day. He can choose from 6 different shirts, 4 different pairs of pants, and 8 different socks. If an 45. outfit consists of 1 shirt, 1 pair of pants, and 2 socks, how many different outfits could he choose? √ 672 674 675 676 673 46. A certain bank issues 4-digit identification codes to its customers using numbers 0, 1, 2,..., 9. How many different codes are possible? √ 10,000 10,0 10, 10,0000 10,00 A menu offers 4 choices for the first course, 5 choices for the second course, and 2 courses for dessert. How many different meals, 47. consisting of a first course, a second course, and a dessert, can one choose from this menu? √ 40 42 43 44 41 A restaurant’s fixed-price special dinner consists of an appetizer, an entrée, and dessert. If the restaurant offers 5 different types of 48. appetizers, 5 different types of entrees, and 4 different types of desserts, how many different ways to order a fixed-price special dinner? 101 103 104 √ 100 102 A certain bank issues 3-letter identification codes to its customers. If each letter can be used only once per code, how many different 49. codes are possible? √ 15,600 15,602 15,603 15,604 15,601 50. Kareem has 4 sweaters, 6 shirts, and 3 pairs of slacks. How many distinct outfits, each consisting of a sweater, a shirt, and a pair of slacks, can Kareem select?  √ 72 74 75 76 73 51. How many 4-person committees can be formed from a club of 12 members? √ 495 499 498 497 496 52. Of the 40 dogs at the animal shelter, 12 are purebred. If 1 of the 40 dogs is selected at random, what is the probability that it is purebred? √ 30 32 33 34 31 53. 10 people wait in line for a movie. How many different ways can the line be arranged? √ 3,628,800 3,628,802 3,628,803 3,628,804 3,628,801 Pizza Hut offers 15 different toppings. Assuming no topping can be repeated on a single pizza, how many different 3 topping pizzas be 54. created? √ 455 453 452 451 454 55. There are 30 students in a statistics class. How many ways can the teacher pick out a group of 5 students? √ 142,506 142,504 142,503 142,502 142,505 56. In how many ways can a first prize, a second prize and four identical third prizes be awarded to a group of 15 people? √ 150,150 150,152 150,153 150,154 150,151 In a new group of 15 employees at a restaurant, 10 are to be assigned as servers, 3 are to be assigned as hosts, and 2 are to be assigned 57. as cashiers. In how many ways can the assignment be made? √ 30,030  30,032 30,033 30,034 30,031 A 7-card hand is chosen from a standard 52-card deck. How many of these will have four spades and three hearts (remember that there 58. are 13 cards of each suit in a deck)? √ 204,490 204,492 204,493 204,494 204,491 Serial numbers for a product are to be made using three letters (using any letter of the alphabet) followed by two single-digit numbers. 59. For example, JGR29 is one such serial number. How many such serial numbers are possible if neither letters nor numbers can be repeated? √ 1,404,000 1,404,002 1,404,003 1,404,004 1,404,001 There are 20 people who work in an office together. Four of these people are selected to attend four different conferences. The first 60. person selected will go to a conference in New York, the second will go to Chicago, the third to San Franciso, and the fourth to Miami. How many such selections are possible? 116283 √ 116280 116281 116282 116284 There are 20 people who work in an office together. Four of these people are selected to go to the same conference together. How many 61. such selections are possible? √ 4845 4847 4848 4849 4846 62. How many different combinations of 8 numbers are there? √ 40320 6 7 8 5 63. How many combinations can be made with 5 numbers? √ 120 3 4 5 2 64. How many different combinations of 4 items are there?  √ 24 4 5 6 3 65. How many different combinations of 3 numbers are there? √ 6 8 9 2 7 66. The product of all positive integers less than or equal to n is... √ N factorial Number Factor neither Figure 67. Which is an important parameter of permutation? √ Number of items being chosen at a time Some items Part of items neither Only one item 68. A permutation could be referred to as... √ Ordered combination Lag variable Outlier neither Nominal variable 69. Selections of some members of a set where order is disregarded is called... √ Combination Permutation Nomination neither Arrangement 70. An arrangement or ordering of a number of distinct objects is... √ Permutation Branching Order neither Combination There are 6 red, 5 blue, 3 green and 1 yellow marbles in a jar. Jada picks a marble without looking. What is the probability Jada picks a 71. red or yellow marble?  7/12 √ 7/15 7/14 7/13 7/11 72. From a standard deck of cards, find the probability of picking a queen or an even number. √ 6/13 6/16 6/12 6/14 6/15 73. M A T H E M A T I C S ( Each letter represents a card)You select a card at random. Without replacing the card, you select a second card. Find the probability. P(M, then H) 1/52 1/51 √ 1/55 1/54 1/53 You have 15 pennies in your pocket. Of those pennies, 3 are Canadian. Suppose you pick a penny out of your pocket at random. Find 74. P(not Canadian). This is a ___________________________event. complicated √ likely unlikely simple neither 75. A bag contains 4 white buttons. How many black buttons must be added so there is an even chance of picking a white button? 5 √ 4 3 2 1 76. A bag contains just 5 buttons, all of which are blue. What is the probability of picking a red button from the bag? 1 4 3 2 √ 0 77. Something that is unlikely to happen has a probability of between 3 and 4 √ 0 and 0.5 0.5 and 1 1 and 2 2 and 3  From left to right on the number line, order the events based on how likely they are to occur.a. The event is certain to happen.b. The 78. event is just as likely to happen as not to happen.c. The event has no chance of happening.d. The event could happen but is unlikely.e. The event is likely to happen. D, c, b, e, a A, e, b, d, c √ C, d, b, e, a A, c, b, d, e D, c, b, a, e A set of 15 cards is numbered 1, 2, 3, …, 15. Suppose you choose one card at random without looking. What is the probability of 79. choosing an odd-numbered card? √ 8/15 8/13 8/12 8/11 8/14 A spinner numbered 1 through 10 is spun 100 times. The results of the experiment are shown in the table below. What is the 80. experimental probability of spinning an 8? √ 13/100 15/100 16/100 17/100 14/100 81. Spinning a number 6 and then spinning a number 5 on the same spinner. √ Independent Events simple Events complicated Events neither dependent Events 82. A bag contains 3 red cubes, 4 green cubes, and 5 blue cubes. One cube is taken from the bag and is not replaced. Another cube is taken. √ Dependent simple complicated neither independent 83. Landing on heads after tossing a coin and rolling a 5 on a single 6-sided die √ Independent Events simple events complicated events neither dependent events 84. You spend a spinner thrice. What is the probability of P(5, even number, and 1) √ 1/108 1/107 1/106 1/105 1/109 85. You pick a marble at random. When you put the first marble back, you select a second marble at random. What is P(green, orange)?  √ 1/18 1/16 1/15 1/14 1/17 86. In a bag of colored marbles, there are 5 red, 4 blue, and 6 green marbles. If you randomly pick one marble from the bag, what is the probability that it is not blue? √ 11/15 11/13 11/12 11/16 11/14 87. You flip a coin twice. What is P(heads, heads)? 1/2 1/5 1/6 √ 1/4 1/3 In a shooting test, the probability of hitting the target is 1/2 for A and 2/3 for B and 3/4 for C. Find the probability that all of them hit the 88. target. 1/6 1/5 1/2 1/3 √ 1/4 89. In a shooting test, the probability of hitting the target is 1/2 for A and 2/3 for B and 3/4 for C. Find the probability that the target is hit √ 23/24 23/26 23/27 23/28 23/25 90. If 3 cards are drawn simultaneously form a pack of well shuffled cards, find the probability of then being all Queen. √ None of these 26/220 26/222 26/223 26/221 A bag contains four blue, three green and five red balls.If three balls are drawn at random, what is the probability that three is at least 91. one red ball in the three balls? √ 37/44 37/46 37/47 37/48  37/45 A bag contains four blue, three green and five red balls If three balls are drawn at random, what is the probability that all the three balls 92. are of different colors? √ 3/11 3/9 3/12 3/15 3/10 A bag contains four blue, three green and five red balls.If four balls are drawn at random, what is the probability that two are blue and 93. two are green? √ 2/55 2/53 2/52 2/50 2/54 A bag contains four blue, three green and five red balls.If three balls are drawn at random from the bag, then what is the probability that 94. all are red? √ 1/22 1/24 1/25 1/26 1/23 95. A bag contains 7 blue balls and 5 yellow balls. If two balls are selected at random, what is the probability that none is yellow? √ 7/22 7/24 7/25 7/26 7/23 96. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is: √ 1/26 1/24 1/23 1/22 1/25 97. Three unbiased coins are tossed. What is the probability of getting at most two heads? √ 7/8 6/8 5/8 4/8 7/9 98. Two dice are tossed. The probability that the total score is a prime number is: √ 5/12 5/14 5/15 5/16 5/13 99. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings? √ 1/221 2/221 3/221 4/221 1/220 100. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? √ 3/4 3/6 3/7 1/4 3/5 There are 12 boys and 8 girls in a tution centre. If three of them scored first mark, then what is the probability that one of the three is a 101. girl and the other two are boys? 42/95 41/95 √ 44/95 43/95 102. In a class, there are 12 boys and 16 girls. One of them is called out by an enroll number, what is the probability that the one called is a girl? √ 4/7 4/6 3/7 2/7 4/5 103. What is the probability of paper losing to scissors? √ 1/3 1/4 1/5 1/6 1/2 104. There are red, yellow and green lollipops in a bag. What is the probability of selecting a blue one? √ 0/3 1/2 1/4 1/5 1/3 105. If you flipped a coin, what is the probability it will land on heads? √ 1/2 1/3 0 1 1/4 106. What is the probability of rock beating paper?  1/2 2/3 √ 0 1/3 1/4 107. What is the probability of selecting the diamond suit from a deck of playing cards? √ 1/4 1/2 1/5 1/6 1/3 108. A card is selected from a deck of playing cards. What is the probability of selecting a red card? √ 1/2 1/4 1/5 1/6 1/3 109. A lolly bag contains 2 red, 3 green and 2 blue gum balls. What is the probability of selecting a green one? √ 3/7 2/6 2/5 2/4 2/7 110. If you rolled a 6-sided dice, what is the probability of rolling a even number? √ 3/6 2/6 3/4 3/7 3/5 111. If you flipped 2 coins, what is the probability that both will land on tails? √ 1/4 1/5 1/6 1/7 3/4 112. If you rolled a 6-sided dice, what is the probability of rolling a 3? √ 1/6 3/6 5/6 5/7 2/3 113. A jar contains 9 red, 7 blue, and 5 green marbles. If one marble is drawn at random, what is the probability that it is not green?  1/6 √ 2/3 1/3 1/2 none In a game, a spinner is divided into 8 equal sections numbered 1 to 8. What is the probability that the spinner lands on a number greater 114. than 5? √ 0.5 0.3 0.2 none 0.4 A box contains 10 red, 8 blue, and 6 green marbles. If two marbles are drawn at random without replacement, what is the probability 115. that they are of different colors? √ 31/45 31/90 1/2 none 1/5 116. A deck of 52 cards is shuffled and one card is drawn. What is the probability that the card is a diamond or a face card? √ 11/26 1/26 1/12 none 1/11 117. A fair die is rolled twice. What is the probability that the first roll is an even number and the second roll is an odd number? √ 1/4 1/2 1/5 none 1/3 A jar contains 6 red, 5 green, and 4 blue marbles. If three marbles are drawn at random without replacement, what is the probability that 118. at least one marble is red? √ 0.75 0.25 0.1 none 0.5 119. A classroom has 12 boys and 18 girls. If three students are selected at random, what is the probability that all three are girls? none 1/67 1/2 1/5 √ 51/190 A box contains 8 red, 6 blue, and 4 green balls. If two balls are drawn at random without replacement, what is the probability that one is 120. red and the other is blue? √ 28/85  1/2 1/6 none 1/8 In a deck of 52 cards, two cards are drawn at random without replacement. What is the probability that the first card is a queen and the 121. second card is a king? √ 1/221 1/22 1/6 none 1/2 122. A classroom contains 10 boys and 15 girls. If three students are selected at random, what is the probability that all three are boys? √ 2/91 1/6 1/7 none 1/2 123. A coin is tossed 6 times. What is the probability of getting exactly 4 heads? √ 15/64 1/5 1/2 none 1/6 124. A single card is drawn from a standard deck of 52 cards. What is the probability that it is either a spade or an ace? √ 4/13 1/13 1/52 none 1/4 A jar contains 5 red, 3 blue, and 2 green marbles. If two marbles are drawn at random with replacement, what is the probability that both 125. marbles are red? √ 0.25 0.5 0.1 none 0.2 A box contains 4 red, 5 blue, and 7 yellow balls. If two balls are drawn at random without replacement, what is the probability that both 126. balls are yellow? √ 7/40 1/4 1/28 none 1/7 127. A deck of 52 cards is shuffled and two cards are drawn. What is the probability that both cards are of the same suit? √ 4/17 1/4  1/52 none 1/17 A box contains 5 apples, 3 oranges, and 4 bananas. If three fruits are drawn at random without replacement, what is the probability that 128. they are all apples? √ 1/44 1/3 1/4 none 1/12 129. A die is rolled twice. What is the probability that the sum of the numbers rolled is greater than 8? √ 5/18 1/18 1/6 none 1/5 130. A family has 3 children. What is the probability that they have exactly 2 boys? 1/8 1/3 √ 3/8 none 1/24 131. A classroom contains 6 boys and 9 girls. If two students are selected at random, what is the probability that both students are girls? √ 1/3 1/6 1/12 none 1/2 132. A card is drawn at random from a standard deck of 52 cards. What is the probability that the card is a face card (Jack, Queen, or King)? √ 3/13 1/13 1/6 none 1/3 A jar contains 5 red, 4 green, and 3 blue marbles. If three marbles are drawn at random without replacement, what is the probability that 133. all three marbles are of different colors? √ 9/55 1/4 1/3 none 1/9 A committee of 4 is to be formed from 6 men and 5 women. What is the probability that the committee will consist of exactly 2 men and 134. 2 women? √ 9/22 1/11 1/22  none 1/9 135. A jar contains 4 red, 5 blue, and 6 yellow marbles. If a marble is drawn at random, what is the probability that it is not yellow? 1/3 √ 2/3 1/6 none 1/2 A school has 60 students, of which 35 are boys and the rest are girls. If a student is selected at random, what is the probability that the 136. student is a girl? √ 5/12 1/5 1/6 none 1/12 137. A single card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king? √ 17/52 1/52 1/4 none 1/17 A box contains 12 light bulbs, of which 3 are defective. If two bulbs are selected at random without replacement, what is the probability 138. that both bulbs are defective? √ 1/22 1/3 1/2 none 1/4 A committee of 4 people is to be formed from a group of 7 men and 5 women. What is the probability that the committee will consist of 139. exactly 2 men and 2 women? √ 25/77 1/5 1/4 none 1/7 A jar contains 8 red, 6 blue, and 6 green marbles. If two marbles are drawn at random with replacement, what is the probability that both 140. marbles are blue? √ 9/49 1/49 1/4 none 1/9 141. A card is drawn from a standard deck of 52 cards. What is the probability that it is either a face card or a heart? √ 11/26 1/26 1/37 none  1/11 142. A deck of 52 cards is shuffled and one card is drawn. What is the probability that the card is a king or a club? √ 4/13 1/4 0.1 none 1/13 143. A classroom contains 10 boys and 15 girls. If a student is selected at random, what is the probability that the student is a boy? √ 0.4 0.2 0.3 none 0.1 A bag contains 4 red, 3 blue, and 2 green marbles. If two marbles are drawn at random with replacement, what is the probability that 144. both marbles are the same color? √ 25/81 1/81 1/17 none 1/25 145. A fair coin is tossed 4 times. What is the probability of getting exactly 2 heads? √ 3/8 2/7 1/5 none 1/6 A box contains 5 pens and 7 pencils. If three items are selected at random without replacement, what is the probability that all three are 146. pencils? √ 2/77 1/5 1/7 none 1/18 A committee of 5 is to be formed from 6 men and 4 women. What is the probability that the committee will consist of exactly 3 men and 147. 2 women? √ 3/7 1/8 1/6 none 1/7 148. In a lottery, there are 10 prizes and 90 blanks. A lottery ticket is drawn at random. What is the probability of getting a prize? √ 1/10 2/7 1/6 none 1/9 149. A coin is tossed 3 times. What is the probability of getting at least one head? √ 7/8 1/8 1/4 none 1/6 150. Two dice are rolled. What is the probability that the product of the numbers rolled is even? √ 3/4 1/3 1/6 none 1/2 A jar contains 8 red, 7 blue, and 5 yellow marbles. If three marbles are drawn at random without replacement, what is the probability 151. that all three marbles are red? √ 56/969 1/55 2/17 none 1/8 152. A school has 60% boys and 40% girls. If a student is selected at random, what is the probability that the student is a boy or a girl? √ 1 0.4 0.3 none 0.6 153. A card is drawn at random from a standard deck of 52 cards. What is the probability that the card drawn is either a queen or a heart? √ 5/13 1/13 1/6 none 1/12 A bag contains 4 white, 5 black, and 6 red balls. If two balls are drawn at random without replacement, what is the probability that both 154. balls are black? √ 2/33 1/7 1/6 none 1/10 155. A die is rolled twice. What is the probability that the sum of the numbers rolled is 7? √ 1/6 1/2 1/4 none 1/5  A box contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability that it is either red or 156. green? √ 0.7 0.2 0.3 none 0.5 157. A batch of cookies includes 10% that are burnt. If you randomly select 12 cookies, what is the probability that none are burnt? 0.3 none √ 0.2824 0.56 0.876 In a class of 30 students, 15 have done their homework. If 5 students are chosen at random, what is the probability that exactly 3 have 158. done their homework? 0.1 0.376 none √ 0.3267 0.25 159. A student answers 10 true or false questions by guessing. What is the probability that the student gets more than 8 questions correct? √ 0.0547 none 0.8 0.56 0.2 A fair coin is flipped and a six-sided die is rolled. What is the probability that the coin lands on heads and the die shows a number 160. greater than 4? none 0.2 √ 1/6 1/3 0.5 A car alarm goes off 95% of the time when there's a break-in and 10% of the time when there's no break-in. If break-ins are rare (1% 161. chance), what is the probability that there has been a break-in if the alarm has gone off? none √ 0.0867 0.65 0.8 0.1 162. When a fair coin is flipped three times, what is the probability of getting exactly two heads? √ 3/8 none 1/24 1/3 1/8  A bag contains 4 red and 5 green marbles. If two marbles are drawn randomly without replacement, what is the probability that both 163. marbles are green? none 0.1 1/6 1/3 √ 2/9 164. If two people each pick a card randomly from a deck of 52 cards, what is the probability that they pick cards of the same suit? 0.5 √ 0.25 0.1 none 0.2 165. If a standard six-sided die is rolled twice, what is the probability that the sum of the rolls equals 7? 0.3 none √ 1/6 1/3 0.6 A box contains 6 white and 4 black balls. Two balls are drawn randomly. What is the probability that both are white if the drawing is 166. without replacement? 0.1 √ 0.3 none 0.4 0.2 During a game, a player spins a spinner that is divided into four equal parts, each colored differently: red, blue, green, and yellow. What 167. is the probability that the spinner does not stop on green? √ 0.75 0.25 0.1 none 0.5 168. What is the probability that a leap year selected at random will have 53 Sundays? √ 2/7 0.1 0.2 none 1/7 A bowl contains 8 oranges, 6 apples, and 4 bananas. If a fruit is selected at random, what is the probability it is either an orange or a 169. banana? √ 0.75 0.25 0.1 none 0.5 170. A game involves rolling a single six-sided die. What is the probability of rolling a number less than 5?  √ 2/3 0.1 0.4 none 1/3 171. A jar contains 5 blue, 4 red, and 3 green marbles. What is the probability of drawing a marble that is not green? √ 0.75 0.5 0.1 none 0.25 172. If three coins are tossed, what is the probability of getting exactly two heads? √ 0.375 0.25 0.5 none 0.125 In a drawer full of socks containing 10 identical black socks and 10 identical white socks, what is the probability of picking two socks 173. of the same color without looking? √ 0.5 0.4 0.7 none 0.1 174. What is the probability of drawing a spade from a standard deck of 52 cards? √ 0.25 0.1 0.6 none 0.5 A school lottery has 500 tickets, and a student purchases 10 of them. What is the probability that the student wins if only one ticket is 175. drawn as the winner? √ 0.02 0.3 0.4 none 0.1 A box contains 8 balls, 3 of which are red and 5 are black. If two balls are drawn at random without replacement, what is the probability 176. that both are red? √ 3/28 0.4 0.1 none 1/15 177. If a fair six-sided die is rolled, what is the probability of rolling a number greater than 2?  √ 2/3 0.1 0.5 none 1/3 178. A bag contains an equal number of red, green, and blue balls. If one ball is drawn, what is the probability that it is not blue? √ 2/3 0.2 0.3 none 0.1 A deck of cards has 52 cards consisting of 4 suits. If a card is drawn at random, what is the probability that it is either a heart or a 179. diamond? √ 0.5 0.3 0.1 none 0.4 180. What is the probability of flipping a fair coin three times and getting at least one head? √ 7/8 0.1 0.7 none 1 In a lottery, there are 100 tickets and one winning ticket. If a person buys 10 tickets, what is the probability that they have the winning 181. ticket? 0.2 √ 0.1 none 0.4 0.3 182. Given that a card drawn from a standard deck is a face card, what is the probability that it is a king? √ 1/3 0.4 0.2 none 1/7 183. A couple has two children, and the older child is a girl. What is the probability that both children are girls? √ 0.5 0.1 0.3 none 0.2 184. A box contains 15 apples, 10 of which are red and 5 are green. What is the probability of randomly picking a green apple? √ 1/3 0.1  0.3 none 2/3 185. When two dice are rolled, what is the probability of the sum being either 5 or 10? √ 1/6 0.3 0.7 none 5/6 In a survey, 70% of respondents prefer tea, and 30% prefer coffee. If the preference for tea and coffee are mutually exclusive, what is 186. the probability of a respondent not preferring tea? 0.4 √ 0.3 0.7 0.1 none 187. What is the probability of rolling a number less than 4 on a fair six-sided die? √ 0.5 0.3 0.7 none 0.1 If the probability of event A occurring is 0.20 and the probability of event B occurring is 0.30, what is the probability of either A or B 188. occurring, assuming they are mutually exclusive? √ 0.5 0.4 0.8 none 0.1 189. A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble or a green marble? √ 5/9 0.1 0.3 none 2/9 190. A fair coin is tossed four times. What is the probability of getting exactly two heads? √ 0.375 0.125 0.25 none 0.5 191. What is the probability of drawing a face card (King, Queen, or Jack) from a standard deck of 52 cards? √ 3/13 0.1 0.5 none  2/13 192. What is the probability of rolling an even number or a number greater than 3 on a fair six-sided die? √ 2/3 0.5 0.6 none 1/3 193. In a bag of 10 marbles, 7 are black and 3 are white. What is the probability of drawing two black marbles in a row without replacement? 0.8 √ 21/45 7/45 0.7 none 194. During a game, a player rolls two dice. What is the probability that the total score is either 7 or 11? √ 5/18 0.3 0.5 none 1/7 195. If two independent events, A and B, have probabilities (P(A) = 0.6) and (P(B) = 0.5), what is the probability of (A) or (B) occurring? √ 0.8 none 0.1 0.3 0.5 196. A classroom has 10 boys and 15 girls. If a student is chosen at random, what is the probability the student is not a girl? √ 0.4 none 0.2 0.3 0.1 197. A bag contains 15 balls: 5 red, 5 blue, and 5 green. If one ball is drawn at random, what is the probability of it being red or green? 1/3 0.3 0.5 none √ 2/3 198. What is the probability of drawing an odd number from a fair six-sided die? √ 1/12 none 0.6 0.4 5/12 199. A box contains 5 red, 4 blue, and 3 green marbles. What is the probability of drawing a blue or green marble?  √ 7/12 0.5 1/12 0.3 none 200. What is the probability of drawing either a king or a heart from a standard deck of 52 cards? none √ 4/13 1/13 0.5 0.6 A drawer contains socks of two colors: 8 blue and 12 black. If two socks are drawn at random without looking, what is the probability 201. they are of the same color? 0.6 none √ 37/95 20/78 0.5 202. What is the probability that a single roll of a fair six-sided die will result in a number greater than 4? 0.7 1/7 √ 1/3 none 0.5 203. Two cards are drawn at random from a deck without replacement. What is the probability that both cards are hearts? 0.3 none √ 1/17 2/17 0.5 204. If the probability of an event A is 0.7, what is the probability of the complementary event ? none 0.2 √ 0.3 0.7 1 205. In a lottery, there are 100 tickets and only one winning ticket. What is the probability that a ticket bought is not the winning ticket? none 0.1 1 0.01 √ 0.99 206. What is the probability of drawing an ace or a spade from a standard deck of cards? √ 4/13 none 1/13  2/7 1/4 207. A fair die is rolled twice. What is the probability that the sum of the rolls is 10? 1/8 1/7 1/6 √ 1/12 none 208. A classroom has 12 boys and 18 girls. What is the probability that a randomly selected student is a girl? none 0.4 √ 0.6 0.2 0.1 209. A bag contains 6 blue, 3 red, and 1 yellow marble. What is the probability of drawing a marble that is not yellow? √ 0.9 0.2 none 0.7 0.5 210. Two events, A and B, are independent with (P(A) = 0.4) and (P(B) = 0.3). What is the probability of both A and B occurring?** 0 1 0.5 √ 0.12 none 211. What is the probability of rolling a number less than 5 on a fair six-sided die? 1 √ 2/3 none 1/6 0.5 In a bag of red, green, and blue marbles, the probability of picking a red marble is 1/5, and picking a green marble is 2/5. What is the 212. probability of not picking a blue marble? 0.8 √ 0.6 0.5 0.2 none 213. If a single card is drawn from a standard 52-card deck, what is the probability that the card is a king or a queen? none √ 2/13 1/13 0.5 1 214. A number is selected from the first 20 natural numbers. Find the probability that it would be divisible by 3 or 7? √ 7/20 none 19/46 24/67 12/37 Let there be two newly launched phones A and B. The probability that phone A has good battery life is 0.7 and the probability that 215. phone B has a good battery life is 0.8. Then find the probability that a phone has good battery life. none 0.45 √ 0.75 0.85 0.65 Company A produces 10% defective products, Company B produces 20% defective products and C produces 5% defective products. If 216. choosing a company is an equally likely event, then find the probability that the product chosen is defective. 0.2 none √ 0.12 0.1 0.32 Using the digits 1, 2, 3, 4, and 5, a number having five digits is formed without any repetition. What is the probability that the number is 217. divisible by 4? 2/5 3/5 none 5/6 √ 1/5 218. The probability of selecting a bad egg is 0.035 from the lot of 400 eggs. So, what is the number of bad eggs in the lot? √ 14 none 20 35 17 A stock of pens consists of 144 ball pens in which 20 pens are defective, and others are good. A girl went to the shop to purchase a pen. 219. The shopkeeper randomly draws one pen and gives it to her. What is the probability that a girl will buy the good pen? 1/3 none √ 31/36 1/36 1/6 220. In 30 balls, a batsman hits the boundaries 6 times. What will be the probability that he did not hit the boundaries? 1/20 √ 4/5 1/5 1/4 none  If a number is selected at random from the first 50 natural numbers, what will be the probability that the selected number is a multiple of 221. 3 and 4? 1/10 none √ 2/25 1/25 1/5 222. Suppose a number x is chosen from the numbers -2, -1, 0, 1, 2. What will be the probability of none √ 4/5 1/5 2/3 1 223. A dice is thrown twice. What is the probability of getting two numbers whose product is even? none 1/4 √ 3/4 1/3 1/2 224. If two dice are thrown together, what is the probability of getting an even number on one dice and an odd number on the other dice? √ 1/2 none 4/7 2/5 1/3 225. What will be the probability of losing a game if the winning probability is 0.3? 1 none √ 0.7 0.3 0.5 226. What is the probability of getting 1 and 5 if a dice is thrown once? 1/6 none √ 1/3 1/2 1/36 227. What is the probability of getting a sum as 3 if a dice is thrown? none 1/36 √ 1/18 1/6  1/3 228. What will be the value of P(not E) if P(E) = 0.07? √ 0.93 none 0.07 0.73 0.83 229. An event in the probability that will never be happened is called as: Unsure event none √ Impossible event Possible event Sure event 230. Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King 1/2 none 1/13 1/52 √ 1/26 The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of 231. success of at least two. 1/3 √ 1/6 none 1/4 1/2 A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the 232. probability that the sum of the three numbers on the balls selected from the box will be odd? √ 1/2 none 1/4 1/6 1/3 Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The 233. probability that all the three apply for the same house is : 7/9 none √ 1/9 2/9 8/9 Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected 234. persons will be a girl. none 19/34 √ 25/34 20/34 5/4  In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the 235. probability that he. has offered English or Hindi ? √ 2/5 none 4/5 3/4 1/2 236. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is: √ 21/46 none 1/50 3/25 1/5 A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what 237. is the probability that either both are oranges or both are non defective? 136/345 none 158/435 17/87 √ 316/435 A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are chosen at random. What is the probability that more than one 238. vowel will be selected ? 13/42 3/14 none 5/42 √ 17/42 Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/9. Find the probability that both 239. of them are selected. √ 2/63 none 1/9 1/63 1/14 In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the 240. probability that he. has offered English or Hindi ? 4/5 √ 2/5 1/2 3/4 none In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor 241. green? 3/5 none √ 1/3 5/21  8/21 A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the 242. probability of wife's selection is (1/5). What is the probability that only one of them is selected ? 3/4 none 4/5 √ 2/7 3/7 243. Two dice are tossed. The probability that the total score is a prime number is: none 1/12 1/6 1/5 √ 5/12 244. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? 1/2 none √ 2/7 5/7 1/5 245. Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen? √ 55/221 none 18/221 55/190 5/221 Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number 246. which is a multiple of 3 or 5? none 1/7 7/20 3/20 √ 9/20 A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the 247. problem will be solved? 1/12 none √ 3/4 1/3 1/4 248. A fair coin is tossed three times. Work out the probability of getting two heads and one tail. none 1/8 √ 3/8 1/3 1/24 249. Rachel flips a biased coin. The probability that she gets two heads is 0.16. What is the probability that she gets two tails? √ 0.36 none 0.7056 0.84 0.6 There are 18 girls and 12 boys in a class. 2/9 of the girls and 1/4 of the boys walk to school. One of the students who walks to school is 250. chosen at random. Find the probability that the student is a boy. √ 3/7 none 1/3 1/7 12/30 A restaurant offers the following options: Starter – soup or salad 251. Main – chicken, fish or vegetarian Dessert – ice cream or cake How many possible different combinations of starter, main and dessert are there? 7 √ 12 none 15 8 Arthur asked the students in his class whether they like math and whether they like science. He recorded his results in the Venn diagram 252. below. How many students don’t like science? 6 none √ 16  23 7 Alice has some red balls and some black balls in a bag. Altogether she has 25 balls. Alice picks one ball from the bag. The probability 253. that Alice picks a red ball is x and the probability that Alice picks a black ball is 4x. Work out how many black balls are in the bag. 6 none √ 20 100 5 254. Ifan rolls a fair dice, with sides labeled A, B, C, D, E and F. What is the probability that the dice lands on a vowel? none 1/2 √ 1/3 1/4 1/6 Two players, Sangeet and Rashmi, play a tennis match. The probability of Sangeet winning the match is 0.62. What is the probability 255. that Rashmi will win the match? none 0.62 0.3 √ 0.38 0.6 256. One card is drawn from a deck of 52 cards, well-shuffled. Calculate the probability that the card will not be an ace 3/13 none √ 12/13 1/13 2/13 257. One card is drawn from a deck of 52 cards, well-shuffled. Calculate the probability that the card will be an ace √ 1/13 none 1 2/7 1/14 X = {−4,−2,1,3} Y = {−1,4,5}. If x is a number from set X, and y is a number from set Y. The probability that x + y is positive is closest 258. to: 0.1 √ 0.7 none 0.3 1 A jar contains 10 blue, 8 green, and 6 red marbles. Every time a marble is removed from the jar, it is not replaced. What is the 259. probability, to the nearest hundredth, that the second marble chosen is green if the first marble chosen is green? 0.1 none 0.2 0.5  √ 0.3 John buys a cake at a bakery and a hammer at a hard- ware store. If there are five hardware stores and three bakeries, in how many 260. different combinations of stores can he purchase the cake and the hammer? 8 none √ 15 20 10 261. How many positive 4-digit numbers are there with an even digit in the hundreds position and an odd digit in the tens position? 10,000 2,150 √ 2,250 2,500 5,040 60 blue marbles and 40 red marbles are in a jar. How many red marbles must be removed from the jar so that the probability of choosing 262. a blue marble from the jar is 4/3? 15 none √ 20 5 10 263. If Event A and Event B are independent, what does P(A ∩ B) equal? √ P(A) * P(B) P(A) - P(B) None of the above P(A) / P(B) P(A) + P(B) 264. A bag contains 4 red, 5 blue, and 6 green balls. What is the probability of drawing a blue or a green ball? 5/15 √ 11/15 9/15 None of the above 10/15 265. If the probability of an event A is 0.7, what is the probability of its complementary event, A'? 1 0.7 √ 0.3 None of the above 0.6 266. What is the probability of the union of two events A and B, given that P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1? 0.9 √ 0.8 None of the above 0.7  1 267. If two events A and B are mutually exclusive, what is P(A ∩ B)? √ 0 P(A) + P(B) P(A) * P(B) None of the above 1 268. What does the probability of an impossible event equal to? √ 0 1 -1 Cannot be determined 1/2 269. Which of the following is an example of a random experiment? Solving a math problem Reading a book Writing an essay None of the above √ Rolling a dice 270. What is an outcome in the context of probability theory? The process of performing an experiment A type of probability The event None of the above √ The result of an experiment 271. If a single 6-sided die is rolled, what is the probability of rolling a 4? √ 1/6 1/2 1/4 None of the above 1/3 272. What is the probability of flipping a fair coin and it landing on heads? √ 1/2 1/5 1 None of the above 1/3 273. If the probability of an event occurring is 0.2, what is the probability of the event not occurring? 0.2 0.5 0.3 1 √ 0.8 274. If a bag contains 4 red balls and 6 blue balls, what is the probability of drawing a red ball? 3/10 √ 2/5 1/2 3/5 None of the above 275. What does it mean if two events A and B are independent? The occurrence of A increases the probability of B occurring The occurrence of A makes B impossible The occurrence of B is dependent on A not occurring None of the above √ The occurrence of A has no effect on the probability of B occurring 276. If two events A and B are mutually exclusive, what is P(A ∩ B)? √ 0 1 -1 Cannot be determined 0.5 277. In a single toss of a fair coin, what is the probability of getting a head? 0.25 0.75 1 Cannot be determined √ 0.5 278. If P(A) = 0.5, what is the probability of the complement of A? √ 0.5 1 0 Cannot be determined 2 279. The complement of an event A is: The event that A occurs √ The event that A does not occur The sum of all probabilities including A None of the above  The event that A and B occur together 280. The intersection of two events A and B is defined as: The event that either A or B occurs √ The event that both A and B occur The event that A occurs without B occurring None of the above The event that neither A nor B occurs 281. Which of the following represents the union of two events A and B? √ The event that either A or B, or both, occur The event that A occurs if B does not occur The event that B occurs if A does not occur None of the above The event that both A and B occur simultaneously 282. If the probability of an event happening is 1, what does it mean? The event is impossible to occur √ The event is certain to occur The event's occurrence is random None of the above The event might occur 283. The probability of any event is always between: None of the above -1 and 1, inclusive 0 and 100, inclusive -1 and 0, inclusive √ 0 and 1, inclusive 284. An event in probability theory is: Any possible outcome of a random experiment √ A collection of one or more outcomes of a random experiment An unexpected result in an experiment None of the above A specific outcome that a researcher wishes to occur 285. What is an outcome in the context of probability theory? The process of conducting an experiment A prediction made before an experiment The analysis of an experiment after it is done None of the above  √ The result of an experiment 286. Which of the following best describes a random experiment? An experiment that can only be performed once √ An experiment where the outcome cannot be predicted with certainty An experiment performed without any prior planning None of the above An experiment with a guaranteed outcome 287. The number of all the odd divisor is 3600 is √ 9 7 8 2 3 288. Number of triangles that can be formed joining the angular points of decagon is √ 120 236 167 178 234 289. A polygon has 65 diagonals. The number of its sides is √ 13 54 65 76 23 The total number of flags with three horizontal strips, in order that can be formed using 2 identical red, 2 identical green and 2 identical 290. white strips, is equal to: √ 4! 45 65 87 32 Total number of 4 digit number that are greater than 3000, that can be formed using the digits 1,2,3,4,5,6 (no digits is being repeated in 291. any number) is equal to: √ 240 534 365 256 234 292. If letters of the word 'KUBER' are written in all possible orders and arranged as in a dictionary, then rank of the word 'KUBER' will be, √ 67 23 56 78  34 All possible four digit numbers are formed using the digits 0,1,2,3 so that no number has repeated digits. The number of even numbers 293. among them is 31 33 √ None of these 12 13 294. The number of arrangements of the letters of the word CALCUTTA √ 5040 3636 1557 3252 4532 295. The number of 5 digit telephone numbers having at least one of their digits repeated is √ 69760 7654 2375 5376 12345 296. How many words can be made from the letters of the word DELHI, if L comes in the middle in every word √ 24 56 26 58 34 297. In how many ways can five examination papers be arranged so that physics and chemistry papers never come together 65 √ 72 43 32 23 298. Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of head is √ 20 32 21 23 45 299. In how many ways can 5 prizes be distributed among four students when every student can take one or more prizes √ 1024 3245 1244 123445 4564 300. Four dice (six faced) are rolled. The numbers of possible outcomes in which at least one die shows 2 is √ 671 756 896 143 456 301. How many even numbers of 3 different digits can be formed from the digits 1,2,3,4,5,6,7,8,9 (repetition is not allowed) √ 224 577 245 965 346 In how many ways can you distribute 5 identical chocolates to 3 children so that any child can get any number of chocolates from 0 to 302. 5? √ 21 65 63 86 34 303. A man has 9 friends, 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? √ 160 654 456 658 535 In how many ways can 8 directors, vice-chairman, and chairman of a firm be selected at a round table if the chairman has to sit between 304. the vice-chairman and a director? √ 8! * 2 531 846 624 5356 305. In how many ways can you choose one or more of 5 different candies? 58 √ 31 53 62 74 306. 12 people at a party shake hands once with everyone else in the room. How many handshakes took place? √ 66 23 45 24 74 307. How many ways can the letters of the word TREES be ordered such that each ‘word’ starts with a consonant and ends with a vowel?  43 √ 18 98 76 56 How many 4-letter words, with or without meaning, can be formed out of the letters of the word, ‘LOGARITHMS’ if repetition of 308. letters is not allowed? √ 5040 2356 5689 3425 5667 309. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there? 253 √ 209 235 455 788 310. In how many ways can the letter of the word ‘PARISE’ be arranged so that no two vowels come together 546 453 567 876 √ 144 Four boys and three girls are to be seated for a dinner such that no two girls sit together and no two boys sit together. Find the number of 311. ways in which this can be arranged. √ 144 253 876 457 346 312. There are 35 teachers in a school. In how many different ways one principal and one vice principal can be chosen? 3466 √ 1190 6346 1234 3244 313. A student has 5 pants and 8 shirts. The number of ways in which he can wear the dress in different combinations is: 65 √ 40 45 87 76 314. Find the number of ways in which 5 players out of 8 players can be selected from a team.  54 98 √ 56 67 65 315. How many 4-letter codes can be formed using the first 9 letters of the English alphabet if no letter is repeated? 8650 √ 3024 4363 √ 3024 5745 8658 2345 316. In how many ways can 3 people be seated in a row containing 6 seats? √ 120 345 637 178 234 Is the statement "the larger sample size or more often you do an experiment, the closer your results will represent the entire population 317. or predicted theoretical number" true or false? false depends on the event neither both √ True 318. Which of the following formulas is used to find the probability of rolling a 2 or landing on tails? P(A) + P(B) P(B/A) P(A) P(A) x P(B/A) √ P(A) x P(B) 319. If P(A) > P(B), then event A is more likely to occur then event B. √ True both depends on the event neither false 320. Events are independent if the occurrence of one event does not affect the probability of the other. both depends on the event neither false √ True  On a game show, the game that a contestant plays is chosen by spinning a spinner. The spinner has 5 colors on it: red, green, blue, 321. purple, and orange. What is the complement of spinning a red or orange on this spinner? (Remember: complement = NOT) purple, blue Green √ Green, purple, blue blue Green, purple 322. If a month is picked at random, what is the probability that the month will start with M? √ 1/6 1/10 1/9 1/8 1/7 There are 20 marbles in a bag, 4 blue, 4 green, 4 red, 4 white and 4 black. Remember that all fraction answers should be given in the 323. simplest form. What is the probability of drawing a black or white marble? 2/8 2/9 √ 2/5 2/6 2/7 There are 5 basketballs, 4 soccer balls and 6 footballs in a ball bin. If a student chooses a ball at random from the bin, what is the 324. probability the student will pick a football or a basketball? 11/16 11/18 11/19 11/17 √ 11/15 Tre has 5 t-shirts, 4 dress shirts and 3 polo shirts in his closet. If he reaches in without looking what is the probability he will pick a t- 325. shirt or a polo shirt? 8/12 , 2/6 √ 8/12 , 2/3 8/12 , 2/4 8/12 , 2/5 8/12 , 2/7 There are 10 red, 5 blue, 3 green and 2 yellow marbles in a jar. Mark picks a marble without looking. What is the probability Mark 326. picks a green or yellow marble? 1/7 1/5 √ 1/4 1/6 1/8 327. Jalen rolls a six sided number cube (a dice). What is the probability that the number rolled is a 2 or a number greater than 3? √ 2/3 2/7 2/6 2/5 2/4 328. From a standard deck of cards, find the probability of picking a heart or spade. 1/6 1/4 √ 1/2 1/3 1/5 A teacher has 9 red crayons, 4 blue crayons, 7 purple crayons, and 5 black crayons in a basket. A student reaches into the basket and 329. randomly selects a crayon. What is the probability that the crayon will be either red or purple? √ 16/25 16/29 16/28 16/27 16/26 A teacher has 9 red crayons, 4 blue crayons, 7 purple crayons, and 5 black crayons in a basket. A student reaches into the basket and 330. randomly selects a crayon. What is the probability that the crayon will be either blue or black? √ 9/25 9/21 9/22 9/23 9/24 331. Scott rolls a six sided number cube (a dice). What is the probability that the number rolled is an even or a 5? √ 2/3 2/7 2/9 2/11 2/5 332. How many ways can you arrange the letters in the word "BOOK"? √ 24 36 48 none 12 333. How many ways can you choose 2 desserts from a menu of 6 desserts? √ 15 20 30 none 12 334. How many different ways can 3 students be seated in a row from a group of 5 students? √ 60 20 120 none 15 335. How many ways can you select 2 marbles from a bag containing 4 red, 3 blue, and 5 green marbles?  √ 66 36 78 none 10 336. How many different 2-letter combinations can be made from the letters A, B, C, and D? √ 12 8 10 none 6 337. How many ways can you choose 4 out of 7 different toppings for a pizza? √ 35 28 14 none 21 338. How many ways can you choose 3 items from a menu of 5 items? √ 10 30 40 none 20 339. How many ways can you choose 2 out of 4 different books to take on a trip? √ 6 8 12 none 4 340. How many ways can 5 students line up in a row? √ 120 240 720 none 60 341. In how many ways can you choose 3 different colors from a palette of 8 colors? √ 56 72 84 none 24 342. A restaurant offers 5 appetizers, 4 main courses, and 3 desserts. How many different three-course meals can be made? 5 √ 60 30  15 none 343. How many ways can a team of 2 be chosen from a group of 6 people? 12 18 30 none √ 15 344. How many different ways can you arrange the letters in the word "PEAR"? 12 36 48 none √ 24 345. A restaurant menu has 3 appetizers, 5 main courses, and 4 desserts. How many different three-course meals can be ordered? 12 √ 60 120 none 30 346. How many ways can 6 different books be arranged on a shelf if there are no restrictions on the arrangement? 360 120 240 none √ 720 347. How many ways can you distribute 5 identical apples to 3 children? √ 7 9 10 none 8 348. A locker combination consists of 3 digits from 0 to 9. How many different combinations are possible if repetition of digits is allowed? 500 900 √ 1000 none 600 349. How many ways can you pick 2 out of 7 different colors? √ 21 35 42 none 28 350. In how many ways can a president and a vice-president be chosen from a group of 5 people?  5 √ 20 30 none 10 351. How many ways can you arrange the letters in the word "BALL"? 12 36 48 none √ 24 352. A restaurant menu offers 3 appetizers, 4 main courses, and 2 desserts. How many different three-course meals can be ordered? 12 √ 24 none 9 18 353. How many ways can you choose 3 letters from the set {A, B, C, D} if the order does not matter? √ 4 8 12 none 6 354. How many ways can you choose 2 out of 4 desserts? √ 6 4 none 12 8 355. How many ways can 4 students line up in a row for a photo? 12 √ 24 32 none 16 356. How many different outcomes are possible when flipping a coin 4 times? none 8 12 √ 16 4 357. How many ways can you arrange the letters in the word "DOG"? 3 9 12  none √ 6 358. How many ways can 2 students be chosen from a class of 6 students? 10 √ 15 20 none 12 359. If you roll a six-sided die, how many possible outcomes are there? 5 7 12 none √ 6 360. How many different 3-digit numbers can be formed using the digits 1, 2, and 3 without repetition? 3 9 12 none √ 6 361. How many ways can you select 3 fruits from a basket containing 5 different types of fruits? 5 15 20 none √ 10 362. How many ways can 2 people be chosen from a group of 5? 5 20 25 none √ 10 363. How many different 2-letter combinations can be made from the letters A, B, and C? 3 9 12 none √ 6 364. How many ways can you choose 1 apple from a basket of 5 apples? 1 10 20 none √ 5 365. How many ways can you flip a coin 3 times and get exactly 2 heads?  √ 3 5 6 none 4 366. You have 4 different shirts and 3 different pairs of pants. How many different outfits can you make? √ 12 24 10 none 6 367. How many ways can 5 books be arranged on a shelf? √ 120 24 12 none 60 368. In how many ways can you choose 2 ice cream flavors from 5 available flavors? √ 10 20 25 none 15 369. How many ways can a committee of 3 be chosen from a group of 10 people? √ 120 100 60 none 720 370. A password consists of 4 digits, where each digit can be any number from 0 to 9. How many different passwords can be created? √ 10K 1K 6K none 9K 371. How many different ways can you arrange the letters in the word "CAT"? √ 6 2 12 none 3 372. How many different ways can you arrange the word "BEAN" where all letters are used? 10 √ 24 12  none 5 373. A pin number consists of four digits (0-9). If the digits can be repeated, how many different pin numbers are possible? none √ 10k 2k 20k 9k 374. If you have five different books and you want to select two to take on a trip, how many different pairs of books can you choose? none √ 10 20 25 5 You have 4 different keychains. If you want to hang 3 of them in a row on your backpack, how many different arrangements can you 375. make? √ 24 none 4 6 12 376. What is the number of ways to arrange the letters in the word "TOO"? 4 √ 3 6 12 none 377. How many ways are there to choose 3 members from a team of 5 to work on a project? 20 none 30 5 √ 10 378. How many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 if no digit is repeated in a number? 120 30 none 80 √ 60 If there are 3 roads to travel from city A to city B and 4 roads to travel from city B to city C, how many different routes can you take to 379. travel from city A to city C via city B? √ 12 none 9 5 7 380. What is the probability of the random arrangement of letters in the word "UNIVERSITY" and two I's should come together? none 1/7 3/5 √ 1/5 2/7 381. In how many ways can we paint the six faces of a cube with six different colours? none 6 √ 30 5 25 382. There are 10 true-false questions in an examination. These questions can be answered in: 100 20 none √ 1024 512 383. The number of ways 4 boys and 3 girls can be seated in a row so that they are alternate is: none √ 144 100 95 57 384. The number of ways in which 8 students can be seated in a line is: 64 none √ 40320 8 20560 A bag contains 50 tickets numbered 1,2,3,4......50 of which five are drawn at random and arranged in ascending order of magnitude.Find 385. the probability that third drawn ticket is equal to 30. √ 551/15134 552/15379 none 1/9 1/2 A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what 386. is the probability that either both are oranges or both are non defective? √ 316/435 none 136/345 158/435 17/87 387. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:  none 1/22 √ 2/91 3/22 2/77 A certain communication system is made up of 40 symbols. A maximum of two symbols placed together, order not mattering, make up 388. a word. What is the maximum number of words in this communication system? √ 840 none 800 125 120 A dart is thrown randomly at the target below. The radius of the innermost circle is 2, and the radius of each circle doubles as the circles 389. get bigger. What is the probability the dart will hit the shaded region, to the nearest hundredth of a percentage? 1.5 none  √ 0.8 1.2 1 Seventy people are seated at a dinner party. Each table at the party can seat eight people. What is the minimum number of tables needed 390. for the party? √ 9 12 none 10 8 A teacher gives stickers to students as a reward for good work. The stickers are on a long strip and re- peat in a regular order: Balloon, 391. Happy Face, Clown Face, and Spaceship. What are the 63rd and 65th stickers handed out by the teacher? √ Clown face and Balloon Balloon and Happy Face Balloon and Spaceship Clown Face and Happy Face Spaceship and Clown Face Five people, all different ages, are arranged in a row so that the oldest person is in the middle and the two youngest people are on the 392. ends. How many differ- ent arrangements of this type exist? 12 none 2 √ 4 8 Someone writes a five digit numeral that reads the same from left to right as right to left (a palindrome). How many 5-digit palindromes 393. are there? √ 900 none 5 250 200 394. How many 5-digit numerals have 9 as the first digit, 3 or 6 as the third digit, and no digit repeated? none 296 √ 672 375 150 From a group of 8 women and 6 men, a committee of 5 people is to be formed. How many different committees are possible if the 395. committee must consist of 3 women and 2 men? 56 none √ 840 560 15 A pizza place offers 8 different toppings. How many ways can a pizza be ordered with any combination of these toppings (excluding a 396. pizza with no toppings)? 128  none √ 255 256 64 397. How many different 4-letter sequences can be formed from the letters of the word "LOGIC" if each letter can only be used once? none 100 5 √ 120 60 How many different ways can a 6-member jury be selected from a pool of 12 men and 8 women if the jury must contain exactly 4 men 398. and 2 women? none 10200 3670 1860 √ 13860 399. In a race with 10 runners where no ties are allowed, how many ways can the first, second, and third place be decided? 60 none √ 720 1000 120 400. How many different 7-digit telephone numbers can be made if the first digit cannot be 0 and repetition is allowed? 1000 none of the above √ 9,000,000 10,000,000 10,000 401. In how many ways can 5 books be arranged on a shelf if 2 specific books must be together? √ 48 24 96 None of the above 120 402. If a 4-member relay team is to be formed from a group of 10 athletes, how many different teams can be formed? 24 None of the above √ 210 5040 120 403. A bag contains 6 red, 4 blue, and 5 green balls. If 3 balls are picked at random, what is the total number of possible outcomes? None of the above 364 15 120  √ 455 404. How many different 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5, if repetition is not allowed? √ 120 none of the above 5 60 24 405. How many ways can a committee of 3 be formed from a group of 8 people if one person must be the chairperson? 56 None of the above √ 168 21 336 If a password must consist of 2 letters followed by 2 digits, and letters can be repeated but digits cannot, how many unique passwords 406. are possible? None of the above 650 √ 60840 5200 1352 407. In how many ways can a president and vice-president be chosen from a team of 6 people? 15 None of the above √ 30 12 36 408. How many ways can 5 different books be arranged on a shelf? 10 25 5 √ 120 60 409. What is 0! (zero factorial)? √ 1 None of the above Undefined Infinity 0 410. From a group of 4 people, how many ways can you choose 2 to form a team? √ 6 10 12 8 4 411. How many different ways can the letters of the word "TOY" be arranged?  12 None of the above 3 √ 6 9 412. What is the probability of selecting the diamond suit from a deck of playing cards? √ 1/4 1/7 1/6 1/5 1/8 413. A card is selected from a deck of playing cards. What is the probability of selecting a red card? √ 1/2 1/6 1/3 1/5 1/4 414. A lolly bag contains 2 red, 3 green and 2 blue gum balls. What is the probability of selecting a green one? 3/8 3/5 3/6 √ 3/7 3/9 415. If you rolled a 6-sided dice, what is the probability of rolling a even number? √ 3/6 3/9 3/5 3/8 3/7 416. If you flipped 2 coins, what is the probability that both will land on tails? √ 1/4 1/5 1/6 1/7 1/8 417. If you rolled a 6-sided dice, what is the probability of rolling a 3? 1/9 √ 1/6 1/8 1/7 1/5 A card is drawn at random from a normal pack of 52 cards. If A represents the event that the card drawn is a Queen and B represents the 418. event that the card drawn is a Heart. Find P(A|B).  √ 4/13 4/14 4/17 4/16 4/15 A computer generates 4-digit random numbers in the range 0000 to 9999 inclusive. Find the probability that the computer produces a 419. random number that begins and ends with the digit 1. 1/10 1/100000 1/10000 √ 1/100 1/1000 An interview with 18 people revealed that 5 of the 8 women and 8 of the 10 men preferred drinking coffee to tea. What is the probability 420. that if one person is selected from the group of 18 people, it is either a woman or someone who preferred to drink coffee than tea? 8/12 8/13 √ 8/9 8/10 8/11 A bag contains 30 balls. The balls are numbered 1,2,3,4 ….30. A ball is drawn at random. Find the probability that the number on the 421. ball is a prime number. 1/6 1/5 1/4 √ 1/3 1/7 422. Two fair dice, one red and one blue, are tossed. What is the probability that the total of the numbers shown by the two dice exceeds 3? √ 11/12 11/17 11/15 11/14 11/13 A man tosses two fair dice. One is numbered 1 to 6 in the usual way and the other is numbered 1, 3, 5, 7, 9 and 11. Find the probability 423. that the total of the two numbers shown is greater than 10. √ 5/12 5/17 5/16 5/15 5/13 I have two 10-cent coins, three 20-cent coins, four 50-cent coins and five $1 coins in my pocket. If I choose a coin at random, find the 424. probability that the coin is worth at least 50 cents. √ 9/14 9/19 9/17 9/16 9/15 The letters of the word “PROBABILITY” are written on cards and the cards are then shuffled. If a card is picked at random, find the 425. probability that it will contain a vowel.  √ 4/11 4/15 4/14 4/13 4/12 One of the 5 points (3, 2), (2, 1), (1, - 4), (5, 5) and (4, 6) is selected at random. What is the probability that it lies on the straight line 3x 426. – 2y = 5? 0.1 √ 0.4 0.3 0.2 0.5 427. An identity card is picked at random. What is the probability that the sum of the last two digits of its number is 9? 0.5 0.4 0.3 0.2 √ 0.1 A box contains 36 marbles. If a marble is picked at random, the probability of being red is 2/9. How many red marbles should be added 428. to make this probability 1/3? 9 2 8 7 √ 6 The letters of the name SMISS are arranged in a line. If an arrangement is chosen at random, what is the probability that the three Ss are 429. together? √ 0.3 0.4 0.5 0.6 0.7 In a survey, 45% of respondents said they like coffee, 30% said they like tea, and 20% said they like both. If a respondent is chosen at 430. random and likes tea, what is the probability that the respondent also likes coffee? 1/3 √ 2/3 none 1/6 1/2 A company has two divisions, A and B. Division A produces 70% of the total products, and division B produces 30%. The defect rates 431. for divisions A and B are 4% and 6%, respectively. If a product is selected at random and is found to be defective, what is the probability that it was produced by division A? 3/5 none √ 14/29 7/15 2/3  A medical test for a certain disease is 95% accurate, meaning that it correctly identifies the presence of the disease 95% of the time and 432. correctly identifies the absence of the disease 95% of the time. If 1% of the population actually has the disease, what is the probability that a person has the disease given that they tested positive? none √ 1/11 1/22 1/33 1/44 In a class of 30 students, 18 students are enrolled in an art class, and 12 are enrolled in a music class. If 5 students are enrolled in both 433. classes, what is the probability that a randomly selected student is enrolled in the art class given that the student is enrolled in the music class? 3/5 none √ 5/12 5/18 2/3 In a certain town, 30% of households have a dog, 25% have a cat, and 15% have both a dog and a cat. If a household is selected at 434. random and has a dog, what is the probability that it also has a cat? 0.4 √ 0.5 none 0.2 0.3 A factory has two machines, A and B. Machine A produces 60% of the total output, and machine B produces 40%. The defect rates for 435. machines A and B are 3% and 5%, respectively. If a randomly selected product is found to be defective, what is the probability that it was produced by machine A? 0.2 √ 9/23 1/16 0.1 none A jar contains 6 red, 4 blue, and 5 green marbles. If three marbles are drawn at random without replacement, what is the probability that 436. at least one of them is red? 3/5 none √ 66/91 25/86 1/3 In a school, 70% of the students take part in extracurricular activities, and 40% of the students who take part in extracurricular activities 437. also excel academically. What is the probability that a randomly selected student takes part in extracurricular activities and excels academically? 0.7 none √ 7/20 1/20 0.1 A box contains 5 apples, 7 oranges, and 8 bananas. If two fruits are drawn at random without replacement, what is the probability that 438. both fruits are oranges? none 1/115  2/97 1/86 √ 21/190 In a group of students, 50% study mathematics, 40% study physics, and 30% study both. If a student is known to study mathematics, 439. what is the probability that they also study physics? √ 0.6 none 0.3 0.4 0.5 A bag contains 10 black, 8 white, and 6 yellow balls. If three balls are drawn at random without replacement, what is the probability that 440. the first ball is white, the second ball is black, and the third ball is yellow? 20/799 none √ 40/969 4/153 1/136 In a certain college, 60% of students are enrolled in a mathematics course, 40% in a science course, and 20% in both. If a student is 441. enrolled in a mathematics course, what is the probability that the student is also enrolled in a science course? 1/5 none √ 1/3 1/2 1/4 A bag contains 8 red, 5 blue, and 7 green balls. If three balls are drawn at random without replacement, what is the probability that all 442. three balls are blue? 3/340 √ 5/680 1/34 none 1/68 In a group of students, 40% play football, 30% play basketball, and 20% play both. If a student plays basketball, what is the probability 443. that the student also plays football? none 1/6 √ 2/3 1/3 1/4 A box contains 6 black, 4 white, an