Q.

Two events A and B have probabilities 0.25 and 0.50,respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is

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a

0.39

b

0.25

c

0.11

d

None of these

answer is A.

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Detailed Solution

P(A∪B)=P(A)+P(B)−P(A∩B)=0.25+0.50−0.14=0.61∴ PA′∩B′=P(A∪B)′=1−P(A∪B)=1−0.61=0.39
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Two events A and B have probabilities 0.25 and 0.50,respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is