# NCERT MCQ’s : Class 12 Maths with Answers MCQ Chapter 13 Probability

## NCERT Solutions for Class 12 Maths Chapter 13 Probability MCQ’s with Answers

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## NCERT Maths MCQs for Class 12 Question and Answers Chapter 13 ProbabilityPDF

(a)3/10
(b)1/5
(c)1/2
(d)3/5

Option c – 1/2

(a)3/6
(b)2/6
(c)1/10
(d) 1/5

Option d – 1/5

(a) 0.24
(b) 0.3
(c) 0.48
(d) 0.96

Option c – 0.48

(a)1/2
(b) 3/4
(c) 1/4
(d) 3/12

Option c – 1/4

(a)5/6
(b)5/7
(c)6/7
(d) 1

Option b – 5/7

(a)5/7
(b)2/7
(c)7/2
(d) 7/12

Option d – 7/12

(a)14/17
(b)17/20
(c)12/7
(d)5/7

Option a – 14/17

### Q8.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)35/256
(c)32/256
(d)38/256

Option a – 37/256

### Q9. 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

Option b – 0.2048

(a)11/50
(b)17/50
(c)13/50
(d)22/50

Option a -11/50

(a)5/9
(b)9/2
(c)2/9
(d)8/9

Option c – 2/9

(a)2/5
(b)3/5
(c)4/5
(d)1/5

Option b – 3/5

### Q13. 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)

Option c – 1 – P(A’) P(B’)

### Q14. 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

Option c – 1 – P(A) = P(B)

### Q15. 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

Option c – Both (a) and (b)

### Q16. P(E ∩ F) is equal to

(a) P(E) . P(F|E)
(b) P(F) . P(E|F)
(c) Both (a) and (b)
(d) None of these

Option c – Both (a) and (b)

(a) 4
(b) 3
(c) 2
(d) 1

Option a – 4

### Q18. The variance of random variable X i.e. or var (X) is equal to

(a) E(X2) + [E(X2)2]2
(b) E(X) – [E(X2)]
(c) E(X2) – [E(X)]2
(d) None of these

Option c – E(X2) – [E(X)]2

### Q19. Three balls are drawn from a bag containing 2 red and 5 black balls, if the random variable X represents the number of red balls drawn, then X can take values

(a) 0, 1, 2
(b) 0, 1, 2, 3
(c) 0
(d) 1, 2

Option a – 0,1, 2

(a) 2
(b) -2
(c) 4
(d) -4

Option a – 2

### Q21. If A and B are independent events, then P(A and B) = P(A) + P(B). State true or false.

Option – False, as P(A and B) = P(A) P(B).

Option – 0.86

### Q23. Prove that if E and F are independent events, then the events E and F are also independent.

Option – As E and F are independent events ∴ P(E ∩ F) = P(E)P(F) …(i) Consider, P(E)P(F) = P(E)[1 – P(F)] = P(E) – P(E)P(F) = P(E) – P(E ∩ F) P(E)P(F’) = P(E ∩ F’) ⇒ E and F’ are independent events.

Option – d

Option – a