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NCERT Solutions for class 12 Maths | Chapter 13 - Probability

(1) If the event A and B are independent, then P(A∩B) is equal to
[A] P(a) + P(b)
[B] P(a) – P(b)
[C] P(a). P(b)
[D] P(a) | P(b)
Answer: P(a). P(b)
(2) If two events are independent, then
[A] they must be mutually exclusive
[B] the sum of their probabilities must be equal to 1
[C] (a) and (b) both are correct
[D] None of the above is correct
Answer: None of the above is correct

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(3) If A and B are such that events that P(a) > 0 and P(b) ≠ 1, then P (A’|B’) equal
[A] 1 – P (A|B)
[B] 1 – P(A’|B)
[C]
[D] p(A’) | P(B’)
Answer:
(4) You are given that A and B are two events such that P(b) = 3/5, P(A|B) = 1/2 and P (A∪B) = then P(B|A’) equals
[A] 1/5
[B] 3/10
[C] 1/2
[D] 3/5
Answer: 3/5
(5) If A and B are two events and A ≠ Φ, B ≠ Φ, then
[A] P (A|B) = P (a). P (b)
[B]
[C] P (A + B). P (B|A) = 1
[D] P (A|B) = P (a) | P (b)
Answer:
(6) If P(a) = 4/5 and P(A∩B) = 7/10, then P(B/A) is equal
[A] 1/10
[B] 1/8
[C] 7/8
[D] 17/20
Answer: 17/20
(7) If A, B are two events associated with same random experiment such that P(a) = 0.4, P(b) = 0.8 and P(B/A) = 0.6 then P(A/B) is
[A] 0.3
[B] 0.4
[C] 0.5
[D] 0.6
Answer: 0.3
(8) Two dice are tossed once. The probability of getting an even number at the first dice ora total of 8 is
[A] 1/36
[B] 3/36
[C] 11/36
[D] 5/9
Answer: 5/9
(9) If P(b) = 1/5, P(A|B) = 1/2 and P(A∪B) = 4/5 then P (A∪B)’ + P (A’∪B) =
[A] 1/5
[B] 4/5
[C] 1/2
[D] 3/5
Answer: 3/5
(10) 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
(11) If P(A∩B) = 7/10 and P(b) = 17/20, then P(A|B) equals
[A] 14/17
[B] 17/20
[C] 7/8
[D] 1/8
Answer: 14/17
(12) An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. A consists 4 outcomes, the number of outcomes that B must have so that A and B are independent is
[A] 2, 4 or 8
[B] 36 or 9
[C] 4 or 8
[D] 5 or 10
Answer: 5 or 10
(13) You are given that A and B are two events such that P(b) = 3/5, P(A|B) = 1/2 and P (A∪B) = 4/5, then P(a) equals
[A] 3/10
[B] 1/5
[C] 1/2
[D] 3/5
Answer: 1/2
(14) A pair of dice are rolled. The probability of obtaining an even prime number on each dice is
[A] 1/36
[B] 1/12
[C] 1/6
[D] 0
Answer: 1/36
(15) The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each others when asked to speak ana fact is
[A] 7/20
[B] 1/5
[C] 3/20
[D] 4/5
Answer: 4/5
(16) If P(a) = 2/5, P(b) = 3/10 and P (A∩B) = 1/5, then P (A’|B’). P(B’|A’) is equal to
[A] 5/6
[B] 5/7
[C] 25/42
[D] 1
Answer: 25/42
(17) If A and B are two independent events with P(a) = 3/5 and P (b) = 4/9, then P (A’∩B’) equals
[A] 4/15
[B] 8/15
[C] 1/3
[D] 2/9
Answer: 2/9
(18) Let P (a) = 7/13, P(b) = 9/13 and P (A∪B) = 9/13, Then P(A’|B) is equal to
[A] 6/13
[B] 4/13
[C] 4/9
[D] 5/9
Answer: 5/9
(19) If A and B are any two events such that P(a) + P(b) – P(A∩B) = P(a) then
[A]
[B]
[C]
[D]
Answer:
(20) If A and B are two events such that P(a) ≠ 0 and 1 then
[A]
[B]
[C]
[D]
Answer:

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