Question

The probabilities of two events A and B are 0.3 and 0.6 respectively. The probability that both A and B occur simultaneously is 0.18 Then, the Probability that neither A nor B occurs is

• A. 0.1
• B. 0.28
• C. 0.42
• D. 0.72

Answer 1

The correct option is B 0.28

$\text{Given:}P\left(A\right)=0.3,P\left(B\right)=0.6P(A\cup B)=0.18$

$P(\overline{A}\cap \overline{B})=1-P(A\cup B)$
$=1-\left[P\right(A)+P(B)-P(A\cap B\left)\right]=1-(0.3+0.6-0.18)=1-(0.90-0.18)=0.10+0.18=0.28$