# MCQ Questions for Class 12 Maths Chapter 13 Probability with answers

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Below you will find MCQ Questions of Chapter 13 Probability Class 12 Maths Free PDF Download that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 13 Probability with answers

1. If a, b and c are all distinct and the

(a) abc-1 = 0

(b) abc = 0

(c) abc’= 0

(d) abc = -1

► (d) abc = -1

2. A bag contains 25 tickets numbered from 1 to 25. Two tickets are drawn one after another without replacement. The probability that both tickets will show even numbers is:​

(a) 11/50

(b) 11/24

(c) 13/25

(d) 3/8

► (a) 11/50

3. The conditional probability P(Ei |A) is called a ____ probability of the hypothesis Ei.​

(a) Beyes’

(b) Posteriori

(c) Hypothesis

(d) Causes

► (b) Posteriori

4. If E and F are events then P (E ∩ F) =

(a) P (E ∩ F) P (F|E), P (E) ≠ 0

(b) P (E) P (E|F), P (E) ≠ 0

(c) P (E∪F) P (F|E), P (E) ≠ 0

(d) P (E) P (F|E), P (E) ≠ 0

► (d) P (E) P (F|E), P (E) ≠ 0

5. Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

(a) 27/102

(b) 29/102

(c) 25/102

(d) 23/102

► (c) 25/102

6. In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb is put back in the box before making the second selection. The probability that both the bulbs are not defective is:​

(a) 8/25

(b) 4/5

(c) 16/25

(d) 9/25

► (c) 16/25

7. A die is tossed twice. Getting a number greater than 4 is considered a success. Then the variance of the probability distribution of the number of successes is:​

(a) 4/9

(b) 2/9

(c) 5/9

(d) 1/3

► (a) 4/9

8. Let E and F be events of a sample space S of an experiment, then P(E’/F) = ___

(a) P(E/F)’

(b) P(E’).P(F)

(c) P(E’)/P(F)

(d) 1 – P(E/F)

► (d) 1 – P(E/F)

9. A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

(a) 47/91

(b) 49/91

(c) 4191

(d) 44/91

► (d) 44/91

10. A random variable is a real valued function whose domain is the.

(a) set of integers

(b) set of irrational numbers

(c) sample space of a random experiment

(d) set of real numbers

► (c) sample space of a random experiment

11. A man make attempts to hit the target. The probability of hitting the target is 3/5 . Then the probability that A hit the target exactly 2 times in 5 attempts is:​

(a) 72/3125

(b) 216/625

(c) 144/3125

(d) 144/625

► (d) 144/625

12. Given that the events A and B are such that P(A) = 1/2 P (A ∪ B) = 3/5 and P(B) = p. Find p if they independent.

(a) 1/5

(b) 1/3

(c) 1/4

(d) 1/2

► (a) 1/5

13. The conditional probability of an event E, given the occurrence of the event F

(a) 0 < P (E|F) < 1

(b) 0 ≤ P (E|F) ≤ 1

(c) 0 ≤ P (E|F) < 1

(d) 0 < P (E|F) ≤ 1

► (b) 0 ≤ P (E|F) ≤ 1

14. There are three coins. One is a two headed coin (having head on both faces),another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

(a) 4/9

(b) 2/9

(c) 1/9

(d) 5/9

► (a) 4/9

15. A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)

(a) 2/3

(b) 1/3

(c) 1/2

(d) 1/5

► (c) 1/2

16. If E, F and G are events then P ((E ∪ F)|G) =

(a) P (E|G) + P (G|F) – P ((E ∩ F)|G)

(b) P (E|G) + P (F|G) – P ((E ∩ F)|G)

(c) P (E|G) + P (F|G) – P ((E ∩ F)|F)

(d) P (G|E) + P (F|G) – P ((E ∩ F)|E)

► (b) P (E|G) + P (F|G) – P ((E ∩ F)|G)

17. If E, F and G are events  with P(G) ≠≠ 0 then P ((E ∪ F)|G)  given by

(a) P (E|G) + P (F|G) – P ((E ∩ F)|F)

(b) P (E|G) + P (G|F) – P ((E ∩ F)|G)

(c) P (G|E) + P (F|G) – P ((E ∩ F)|E)

(d) P (E|G) + P (F|G) – P ((E ∩ F)|G)

► (d) P (E|G) + P (F|G) – P ((E ∩ F)|G)

18. Which of the following conditions do Bernoulli trials satisfy?

(a) finite number of dependent trials

(b) infinite number of dependent trials.

(c) infinite number of independent trials

(d) finite number of independent trials

► (d) finite number of independent trials

19. 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) 7/12

(b) 1/4

(c) 1/2

(d) 3/8

► (d) 3/8

20. An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is:​

(a) 1/2

(b) 3/10

(c) 1/10

(d) 3/5

► (a) 1/2

Hope the given MCQ Questions will help you in cracking exams with good marks. These Probability MCQ Questions will help you in practising more and more questions in less time.