Maths MCQs for Class 12 with Answers Chapter 13 Probability

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 13 Probability. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Probability MCQs Pdf with Answers to know their preparation level.

Probability Class 12 Maths MCQs Pdf

1. Let A and B be two given events such that P(A) = 0.6, P(B) = 0.2 and P(A/B) = 0.5. Then P(A’/B’) is
Maths MCQs for Class 12 with Answers Chapter 13 Probability 1

Answer/Explanation

Answer: c
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 4


2. Let A and B be two given independent events such that P(A) =p and P(B) = q and P(exactly one of A, B) = \(\frac{2}{3}\), then value of 3p + 3q – 6pq is
(a) 2
(b) -2
(c) 4
(d) -4

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 6
Maths MCQs for Class 12 with Answers Chapter 13 Probability 7


3. If P(A ∩ B) = 70% and P(B) = 85%, then P(A/B) is equal to
Maths MCQs for Class 12 with Answers Chapter 13 Probability 2

Answer/Explanation

Answer: a
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 8


4. Two dice are thrown once. If it is known that the sum of the numbers on the dice was less than 6 the probability of getting a sum 3 is
Maths MCQs for Class 12 with Answers Chapter 13 Probability 3

Answer/Explanation

Answer: c
Explaination: (c), as favourable cases for sum less than 6 are 10 and favourable for a total of 3 is 2.


5. 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

Answer/Explanation

Answer: a
Explaination: (a), as there are 2 red balls, so maximum ’ red balls can be 2.


6. The probability distribution of the discrete variable X is given as:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 24
The value of k is
(a) 8
(b) 16
(c) 32
(d) 48

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 19


7. Let A and B be two given mutually exclusive events. Then P(A/B) is _________ .

Answer/Explanation

Answer:
Explaination: 0, as P(A ∩ B) = 0 and P(A/B) = \(\frac{P(A \cap B)}{P(B)}\)


8. If A and B are two independent events such that P(A) = \(\frac{1}{7}\) and P(B) = \(\frac{1}{6}\) then P(A’ ∩ B’) is _________ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 5


9. Three persons A, B and C, fire a target in turn. Their probabilities of hitting the target are 0.2,0.3 and 0.5 respectively, the probability that target hit is _________ .

Answer/Explanation

Answer:
Explaination:
0.72, as /^target hit)
= P(at least one hits the target)
= 1 – P( none hits) =1 \(-P(\bar{A} \bar{B} \bar{C})\)


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

Answer/Explanation

Answer:
Explaination: False, as P(A and B) = P(A) P(B).


11. A speaks truth in 70% cases and B speaks truth in 85% cases. The probability that they speak the same fact is ______ .

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 9


12. Given P(A) = 0.4, P(B) = 0.7 and P(B/A) = 0.6. Find P(A ∪ B).

Answer/Explanation

Answer:
Explaination: .
P(B/A) = \(\frac{P(A \cap B)}{P(A)}\)
⇒ 0.6 × 0.4 = P (A ∩ B)
⇒ P(A ∩ B) = 0.24
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.4 + 0.7 – 0.24
= 0.86


13. Given P(A) = \(\frac{1}{2}\) p(B) = \(\frac{1}{3}\) and P(A ∩ B) = \(\frac{1}{6}\). Are the events A and B independent?

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 10


14. Prove that if E and F are independent events, then the events E and F are also independent. [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
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.


15. A die, whose faces are marked 1, 2, 3 in red and 4,5,6 in green, is tossed. Let A be the event “number obtained is even” and B be the event “number obtained is red”. Find if A and B are independent events. [AI 2017]

Answer/Explanation

Answer:
Explaination:
A : number is even, i.e. 2, 4, 6; P(A) = \(\frac{3}{6}\)
= \(\frac{1}{2}\)
B : number is red, i.e. 1, 2, 3; P(B) = \(\frac{3}{6}\)
= \(\frac{1}{2}\)
A ∩ B : number is even and red, i.e. 2;
P(A ∩ B) = \(\frac{1}{6}\)
P(A) × P(B) = \(\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)
As P(A ∩ B) ≠ P(A) . P(B)
Hence, not independent.


16. A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4. [CBSE 2018]

Answer/Explanation

Answer:
Explaination:
A : sum 8, i.e. (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
B : red die number less than 4.
B : (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3).
A ∩ B : (6, 2), (5, 3)
∴ Conditional probability of obtaining sum 8, given that red die resulted in number less than 4.
Maths MCQs for Class 12 with Answers Chapter 13 Probability 11


17. 12 cards numbered 1 to 12 are placed in a box, mixed up thoroughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.

Answer/Explanation

Answer:
Explaination:
Total cards are 12
A : number drawn is more than 3, i.e. 4, 5, 6, …, 12.
B : getting an even number, i.e. 2, 4, 6, 8, 10, 12.
A ∩ B : 4, 6, 8, 10, 12
Maths MCQs for Class 12 with Answers Chapter 13 Probability 12


18. One card is drawn from a well shuffled pack of 52 cards. If E is the event “the card drawn is a king or a queen” and F is the event “the card drawn is an ace or a queen,” then find the probability of the conditional event E/F. [HOTS]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 13


19. Two cards are drawn from a well shuffled pack of 52 cards one after the other without replacement. Find the probability that one of them is a queen and the other is a king of opposite colour.

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 14


20. A coin is tossed thrice and all eight outcomes are assumed equally likely. Let the event E be “the first throw results in head” and event F be “the last throw results in tail”. Find whether events E and F are independent.

Answer/Explanation

Answer:
Explaination:
Sample space
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
E: first throw results in head = {HHH,HHT,HTH,HTT}
F: Last throw result in tail = {HHT, HTT, THT, TTT}
Maths MCQs for Class 12 with Answers Chapter 13 Probability 15


21. Two dice are thrown. Find the probability that the numbers appeared have a sum 8 if it is known that the second die always exhibits 4. [HOTS]

Answer/Explanation

Answer:
Explaination:
A: Sum of the numbers is 8, i.e. {(2,6), (3,5), (4,4), (5,3), (6,2)}
B: the second die always exhibits 4, i.e. {(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)} A ∩ B= {(4, 4)}
Required probability,
Maths MCQs for Class 12 with Answers Chapter 13 Probability 16


22. If P(A)=0.8,P(B)=0.5 andP(B/A)=0.4, find (i) P(A ∩ B) (ii) P(A/B) (iii) P(A ∪ B). [NCERT]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 17


23. The value of k, for which the following distribution is a probability distribution
Maths MCQs for Class 12 with Answers Chapter 13 Probability 23

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 18


24. Find mean (µ) and variance (a2) for the following probability distribution:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 25

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 20
Maths MCQs for Class 12 with Answers Chapter 13 Probability 21


25. A random variable X has a probability distribution P(X) of the following form where k is some number:Determine (i) k (ii) P(X ≤ 2) (iii) P(X ≤ 2) (iv) P(X ≥ 2). [NCERT; Delhi 2019]

Answer/Explanation

Answer:
Explaination:
Maths MCQs for Class 12 with Answers Chapter 13 Probability 22


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