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

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Q. 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

TS EAMCET 2017

Solution:

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 $