Class 12 Maths Chapter 13 Probability Solved Question and Answers

1 A and B are events such that P(A) = 0.4, P(b) = 0.3 and P(A ∪ B) = 0.5. Then P(B’ ∩ A) equals

A 2/3

B 1/2

C 3/10

D 1/5

View Answer

Answer:1/5

2 If P(A) = 0.4, P(b) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) equal to

A 0.24

B 0.3

C 0.48

D 0.96

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Answer:0.48

3 If A and B are two events sue that P(A) = 1/2, P(b) = 1/3, P(A|B) = 1/4 then (A’ ∩ B’) equals

A 1/12

B 3/4

C 1/4

D 3/16

View Answer

Answer:1/4

4 The mean and the variance of a binomial distribution are 4 and 2 respectively. Find the probability of atleast 6 successes.

A 37/256

B 32/255

C 34/259

D 31/256

View Answer

Answer:37/256

5 If the sum of the mean and variance of a binomial distribution is 15 and the sum of their squares is 17, then find the distribution.

A

B

C

D

View Answer

Answer:

6 In a binomial distribution, the sum of its mean and variance is 1.8. Find the probability of two successes, if the event was conducted times.

A 0.2623

B 0.2048

C 0.302

D 0.305

View Answer

Answer:0.2048

7 A pair of dice is thrown 200 times. If getting a sum of 9 is considered a success, then find the mean and the variance respectively of the number of successes.

A 400/9,1600/81

B 1600/81,400/9

C 1600/81,200/9

D 200/9,1600/81

View Answer

Answer:1600/81,400/9

8 If the mean and the variance of a binomial distribution are 4 and, then find P(X ≥ 1).

A 720/729

B 721/729

C 728/729

D 724/729

View Answer

Answer:728/729

9 If the chance that a ship arrives safely at a port is 9/10; find the chance that out of 5 expected ships, atleast 4 will arrive safely at the port.

A 91854/100000

B 32805/100000

C 59049/100000

D 26244/100000

View Answer

Answer:918541/00000

10 A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both clubs. Find the probability of the lost card being a club.

A 11/50

B 17/50

C 13/50

D 19/50

View Answer

Answer:11/50

11 A bag contains 3 green and 7 white balls. Two balls are drawn one by one at random without replacement. If the second ball drawn is green, what is the probability that the first ball was drawn in also green?

A 5/9

B 4/9

C 2/9

D 8/9

View Answer

Answer:2/9

12 A bag contains 4 balls. Two balls are drawn at random and are found to be white. What is the probability that all balls are white?

A 2/5

B 3/5

C 4/5

D 1/5

View Answer

Answer:3/5

13 A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

A 5/8

B 3/8

C 7/8

D 1/8

View Answer

Answer:3/8

14 Two cards from an ordinary deck of 52 cards are missing. What is the probability that a random card drawn from this deck is a spade?

A 3/4

B 2/3

C 1/2

D 1/4

View Answer

Answer:1/4

15 If A and B are two indendent events such that

= 0.75, P(A ∪ B) = 0.65 and P(b) = P, then find the value of P.

A 9/14

B 7/15

C 5/14

D 8/15

View Answer

Answer:8/15

16 If A and B are two independent events, then the probability of occurrence of at least of A and B is given by

A 1 – P(A) P(b)

B 1 – P(A) P(B’)

C 1 – P(A’) P(B’)

D 1 – P(A’) P(b)

View Answer

Answer:1 – P(A’) P(B’)

17 Two events A and B will be independent, if

A A and B are mutually exclusive

B P(A’ ∩ B’) = [1 – P(A)] [1 – P(B)]

C P(A) = P(B)

D P(A) + P(B) = 1

View Answer

Answer:P(A) = P(B)

18 Two balls are drawn one after another (without replacement) from a bag containing 2 white, 3 red and 5 blue balls. What is the probability that atleast one ball is red?

A 7/15

B 8/15

C P(AB) = 1 + P (A’) P(B’) P(A’)

D 5/16

View Answer

Answer:8/15

19 A bag contains 20 tickets, numbered 1 to 20. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.

A 9/38

B 16/35

C 7/38

D 17/30

View Answer