NCERT Solutions for class 12 Maths | Chapter 13 - Probability

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Questions
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

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

Answer:0.48
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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

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

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

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

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

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

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

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

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

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

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

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

Answer:1/4
15 If A and B are two indendent events such that Class 12 Maths Chapter 13 Probability = 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

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)

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

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

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

Answer:9/38
20 If three events of a sample space are E, F and G, then P(E ∩ F ∩ G) is equal to
A P(E) P(F|E) P(G|(E ∩ F))
B P(E) P(F|E) P(G|EF)
C Both (a) and (b)
D None of these

Answer:Both (a) and (b)

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