Probability

Probability of solving a sum correctly by A, B, and C are 1/2, 1/3, and 1/5 respectively

The probability that at least one of them solves it correctly is 19/20

If P(A) = 4/5, P(B) = 2/5, and P(A ∩ B) = 1/2, then P(A' ∩ B') = 1/10

If 3 coins are tossed, the probability of getting 2 heads is 3/8

If P(A) = 0.7, P(B) = 0.4, P(A ∩ B) = 0.3, then P(A ∩ B') = 2/5

If there are 5 red balls and x black balls, and the probability that two balls drawn at random are red is 5/14, then x = 3

If P(A) = 0.25, P(B) = 0.50, P(A ∩ B) = 0.14, then P(A' ∩ B) = 0.39

If a die is thrown, A is the event that the number obtained is greater than 3, B is the event that the number obtained is less than 5, then P(A ∩ B) is 2/5

If P(A) = 0.4, P(B) = x, P(A ∪ B) = 0.7 and A and B are mutually exclusive, then x = 3/10

A bag X contains 2 white and 3 black balls, another bag Y contains 4 white and 2 black balls. If a bag is selected at random and a ball is drawn from it, then the probability for the chosen ball to be white is 7/15

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles 12 through 15. The probability that a marble drawn at random is white and odd numbered is 1/6

Letters in HULULULU are rearranged, probability of all three L together is 3/28

A man speaks truth 2 out of 3 times, picks a number in S={1,2,3,4,5,6,7}, reports it is even, the probability it is actually even is 1/5

A room has 3 sockets for bulbs, 10 bulbs (6 defective), 3 bulbs at random, the probability the room is lit is 5/6

A bag contains 6 white and 4 black balls. Two balls drawn at random. Probability they are of the same colour is 7/15

The probability that three cards drawn from a pack of 52 cards, are all red is 1/17

If P(A) = 1/4, P(B) = 2/5 and P(A ∩ B) = 1/3, then P(A' ∩ B') = 13/20

Five persons chosen at random from 4 men, 2 women, 4 children, the chance that exactly two will be children is 1/21

If A and B are two events defined on a sample space S such that P(A ∩ B) = 1/4, P(A ∪ B) = 5/8, P(B') = 2/3, then P(A) = 13/24

Two cards are drawn from a pack of well shuffled 52 cards without replacement, probability both cards are queens is 1/221

If A and B independent events and P(A)=2/3, P(B)=3/5, then P(A' ∩ B') = 4/15

If A and B are independent events such that odds in favour of A is 2:3 and odds against B is 4:5, then P(A ∩ B) = 2/9

An urn contains 4 red and 5 white balls. Two balls are drawn one after the other without replacement, the probability that both the balls are red is 1/6

If P(A')=0.6, P(B)=0.8, and P(B/A)=0.3, then P(A/B) = 3/20

Two dice are thrown together. The probability that the sum of the numbers is divisible by 2 or 3 is 2/3

If A and B independent events and P(A)=2/5, P(B)=3/5, then P(A' ∩ B) = 4/15

In a single throw of three dice, the probability of getting a sum at least 5 is 51/54

Letters of word 'LOGARITHM' are randomly arranged, probability the arrangements starts with vowel and ends with consonant is 1/9

Odds in favor of drawing a king from a pack of 52 playing cards is 1:12

Suppose 5% men and 0.25% of women have gray hair. A gray hair person is selected at random. If there are equal number of males and females, the probability the person selected is men is 20/21

Two dice are rolled simultaneously, the probability that the sum of the two numbers on the dice is a prime number, is 5/12

Two unbiased dice are thrown. Then the probability that neither a doublet nor a total of 10 will appear is 7/9

A coin is tossed and a die is thrown. The probability that the outcome will be head or a number greater than 4 or both, is 2/3

Two event A and B, P(A ∪ B)=5/6, P(A)=1/3, P(B)=2/3, A and B are independent

First bag contains 3 red and 5 black balls, Second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Probability that one ball is red and the other is black 41/80

Rooms in a hotel are numbered from 1 to 19. Rooms are allocated at random as guests arrive. First guest is given a room which is prime number. Probability that the second guest to arrive is given a room which is a prime number is 7/18

If P(A)=3/10, P(B)=2/5, P(A ∩ B)=1/5, then P(A/B) x P(B/A)=1/12

Probability at least one of events E₁ and E₂ occurs is 0.6. If simultaneous occurrence E₁ + E₂ 0.2, P(E₁) + P(E₂) = 0.4

A family of three children are chosen at random. Probability that the oldest and youngest children are the same gender is 1/2

Five letters are placed at random in five addressed envelopes. Probability that all letters are not dispatched in the respective right envelopes is 119/120

Shelf contains 5 Physics and 3 Biology books and other has 4 Physics and 2 Biology books. Then the probability of drawing a Physics book is 9/14

Three distinct numbers are chosen from first 100 natural numbers, probability all three of them are divisible by both 2 and 3 is 4/1155

A bag contains 5 red balls and 3 green balls. A ball is selected at random and not replaced. A second ball then selected. Probability of selecting one red ball and one green ball is 15/28

A, B, C are three events, one of which and only one can happen. The odds in favor of A are 4:6, odds against B are 7:3, then odds against C are 7:3

Three critics review a book. For the three critics, odds in favor of the books are (5:2), (4:3), and (3:4). The probability that the majority is in favor of the book is 209/343

Two dice are rolled. If both dice have six faces numbered 1, 2, 3, 5, 7, 11, the probability that the sum of the numbers on the uppermost face is prime is 3/7

Three critics review a book. For the three critics the odds in favor of the book are 2:5, 3:4 , and 4:3 respectively. The probability that the majority is in favor of the book is given by 209/343

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is 1/9

Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability of both of them occur together is 0.1

In a class of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. Then the number of newspapers is at least 30

Four persons can hit a target correctly with probabilities 1/2, 1/3, 1/4 and 1/5 respectively. If all hit the target independently, then the probability that the target would be hit is 3/5

There are three events A, B, C, one of which must and only one can happen. The odds are 8:3 against A, 5:2 against B and the odds against C is 43:17k, then the value of k is 1