Question

If $A$ and $B$ are events of the same experiments with $P\left(A\right)=0.2,P\left(B\right)=0.5$, then find the maximum value of $P(A\cap B)$

Answer 1

$P(\overline{A}\cap B)=P\left(B\right)-P(A\cap B)$
And is maximum when
$(A\cap B)$ is $0$
Then
$P(\overline{A}\cap B)=P\left(B\right)=0.5$