Question

Two events A and B have the probabilities 0.25 and 0.5 respectively. The probability that both A and B simultaneously is 0.12. then the probability that neither A and nor B occurs is ___.

• A. 0.13
• B. 0.38
• C. 0.63
• D. 0.37

Answer 1

The correct option is D 0.37

Given: $P\left(A\right)=0.25$
$P\left(B\right)=0.5$
P(A and B simultaneously happening) = 0.12

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)P(A\cup B)=0.25+0.5-0.12=0.63$
$P(\overline{A}\cap \overline{B})=P\overline{(A\cup B)}=1-P(A\cup B)=1-0.63=0.37$