Question

Two events $A$ and $B$ have the probabilities $0.25$ and $0.5$ respectively. The probability that both $A$ and $B$ occur simultaneously is 0.14. Then the probability of neither A nor B occurs is equal to:

• A. $0.61$
• B. $0.39$
• C. $0.29$
• D. $0.19$

Answer 1

The correct option is B $0.39$

$P($neither $A$ nor $B$ occurs$)$
$=P(\overline{A}\cap \overline{B})$
$1-P(A\cup B)$ {By Demorgan law}
$=1-\left(P\right(A)+P(B)-P(A\cap B\left)\right)$
$=1-(0.25+0.5-0.14)$
$=1-0.61=0.39$