Questions and Answers
Which of the numbers that follow could represent a probability? I. 17/15 II. 0.1
Which of the numbers that follow could represent a probability? I. 50% II. 35%
If a die is rolled one time, find the probability of getting a number greater than 6.
If a die is rolled one time, find the probability of getting a number less than 4 or an even number.
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A box contains five blue, eight green, and three yellow marbles. If a marble is selected at random, what is the probability that it is not blue?
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In a classroom, the students are 14 boys and 4 girls. If one student is selected at random, find the probability that the student is a girl.
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Of the next 33 trials on the docket in a county court, 4 are homicides, 11 are drug offenses, 7 are assaults, and 11 are property crimes. If jurors are assigned to trials randomly, what's the probability that a given juror won't get a property crime case?
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Evaluate 8!
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Evaluate the expression (4!)(3!)
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Evaluate the expression 8!/4!2!
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How many different ways can 3 people stand in line at a cash register?
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Evaluate 10P4.
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A. In how many ways can the letters in the word TEXAS be arranged? b. In how many ways can the letters in the word OHIO be arranged?
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Decide whether the selection described is a combination or a permutation. Five club members are chosen to serve on a committee.
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Decide whether the selection described is a combination or a permutation. Three prizes are given to the winners of a race.
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Find both the number of combinations and the number of permutations for the given number of objects. 10 objects taken 7 at a time.
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How many ways can a committee of 3 people be selected from a group of 8 people?
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How many different ways can a college select three applicants for a teaching position from a pool of 20 applicants?
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A teacher has 20 boys and 10 girls in her class. In how many ways can she select 6 of the children to be in a play if she must select 3 boys and 3 girls?
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How many ways can a person select four books, two CDs, and one DVD from ten books, twenty CDs, and five DVDs?
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Draw a tree diagram to determine the sample space when three coins are tossed.
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Three coins are tossed. Find the probability that exactly two coins land tails up.
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Three coins are tossed. Find the probability that all the coins land heads up.
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Three coins are tossed. Find the probability that two or more coins land heads up.
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Three coins are tossed. Find the probability that no more than one coin lands heads up.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 4 of diamonds.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a black card.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a 7.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a red 6.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond or a 10.
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A single card is drawn from an ordinary 52-card deck. Find the probability of getting a diamond and an ace.
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Two dice are rolled. Find the probability of getting a sum greater than 8.
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Two dice are rolled. Find the probability of getting a 5 on one die or on both dice.
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A package contains 14 candy canes, 8 of which are cracked. If 3 are selected, find the probability of getting no cracked candy canes.
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A package contains 15 candy canes, 13 of which are cracked. If 2 are selected, find the probability of getting exactly one cracked candy cane.
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To win a prize, a person must select 4 numbers from 15 numbers without replacement. Find the probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.) Round to four decimal places, if necessary.
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Study Notes
Probability Representation
- Probabilities are values between 0 and 1, inclusive. Only the number 0.1 (II) represents a valid probability as 17/15 exceeds 1.
Basic Probability of Die Rolls
- The probability of rolling a number greater than 6 with a single die is 0, as a standard die has numbers only up to 6.
- The probability of rolling a number less than 4 or an even number on a die is 5/6, including outcomes like 1, 2, 3, 4, and 6.
Marbles and Probability
- In a box with five blue, eight green, and three yellow marbles, the chance of selecting a marble that is not blue is 11/16.
Classroom Gender Probability
- A classroom with 14 boys and 4 girls gives a probability of 2/9 for randomly selecting a girl.
Trials Probability
- In a court with 33 trials, the probability a juror does not get a property crime case is 2/3, accounting for 26 other cases.
Factorial Evaluation
- 8! evaluates to 40,320, representing all possible arrangements of 8 distinct items.
Permutations and Combinations
- To calculate arrangements: (4!)(3!) = 144.
- The expression 8!/4!2! evaluates to 840, representing combinations of groups.
- For 10 objects taken 7 at a time: combinations (10C7) = 120, permutations (10P7) = 604,800.
Committee Selection
- Choosing 3 from 8 people gives 56 combinations.
- Selecting 3 teachers from 20 applicants results in 1,140 arrangements.
- A selection of 6 children (3 boys and 3 girls) from 20 totals 136,800 ways.
Book, CD, DVD Selection
- Selecting 4 books, 2 CDs, and 1 DVD among 10 books, 20 CDs, and 5 DVDs results in 199,500 possibilities.
Coin Toss Probability
- Tossing three coins, the probability of getting exactly two tails up is 3/8.
- The probability that all coins show heads is 1/8; two or more heads appear with a probability of 1/2; no more than one head appears with a probability of 3/8.
Card Drawing Probabilities
- Drawing a 4 of diamonds from a 52-card deck has a probability of 1/52.
- The chance of picking a black card is 1/2, and for a 7, it's 1/13.
- The probability of drawing a red 6 is 1/26; for drawing a diamond or 10, it's 4/13.
- The probability of selecting a diamond and an ace simultaneously is also 1/52.
Dice Rolling Probability
- When rolling two dice, the probability of achieving a sum greater than 8 is 5/18.
- The chance of rolling a 5 on one or both dice is 11/36.
Candy Cane Selection
- From a package of 14 candy canes (8 cracked), the probability of selecting 3 without cracked ones is 0.0549.
- Choosing 2 candy canes from 15 (13 cracked) has a 0.2476 chance of getting exactly one cracked.
Lottery Probability
- If selecting 4 numbers from 15 without replacement, the probability of winning with one ticket is approximately 0.0007.
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Description
Test your understanding of probability concepts with this Math Test 4 quiz. Each question challenges you to identify which numbers can represent probabilities and calculate probabilities from given scenarios. Perfect for reinforcing your math skills!
