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Two events $A$ and $B$ have probabilities $.25$ and $.50$ 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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$0.39$

$0.375$

$0.89$

$0.86$

answer is A.

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Detailed Solution

$\begin{array}{rcl} P (n e i t h e r A n o r B) & = & 1 - P (e i t h e r A o r B) \\ = & 1 - P (A \cup B) \\ = & 1 - \{P (A) + P (B) - P (A \cap B)\} \\ = & 1 - 0.25 - 0.5 + 0.14 \\ = & 0.39 \end{array}$

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