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Assertion:- Two events A and B have probabilities 0.25 and 0.5 respectively. The probability that both A and B occurs simultaneously is 0.14. Then the probability that neither A nor B occurs is 0.39.
Reason :- A and B are any two events then $P (\bar{A} \cap \bar{B}) = 1 - P (A \cup B)$

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A is correct but R is not correct

A is not correct but R is correct

Both A and R are correct and R is the correct explanation of A

Both A and R are correct and R is not the correct explanation of A

answer is C.

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Detailed Solution

$P (A) = 0.25, P (B) = 0.50, P (A \cap B) = 0.14$

$P (A \cup B) = 0.25 + 0.50 - 0.14 = 0.61$

$∴ P (\bar{A} \cap \bar{B}) = 1 - P (A \cup B) = 1 - 0.61 = 0.39$

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