Question

If $A$ and $B$ are events having probabilities, $P(A)=0.6,P(B)=0.4$ and $A\cap B)=0$ , then the probability that neither $A$ nor $B$ occurs is

• A. $\frac{1}{4}$
• B. 1
• C. $\frac{1}{2}$
• D. 0

Answer 1

Answer: (D)

Given, $P(A)=0.6,P(B)=0.4$ and $P(A\cap B)=0$,
then $P$ (neither $A$ nor $B$)$=P(\bar{A}\cap \bar{B})$
$=P(\overline{A\cup B})=1-P(A\cup B)$
$=1-P(A)-P(B)+P(A\cap B)$
$[\because P(A\cup B)=P(A)+P(B)-P(A\cap B)]$
$=1-0.6-0.4+0=1-1=0$