Question

If $A$ and $B$ are two events such that $P\left(A\right)=0.4$ $P\left(B\right)=0.3,$ and $P\left(A\cup B\right)=0.5$. Then find $10P\left(B^{\prime }\cap A\right).$

Answer 1

We want to find that shaded portion $=P(B^{\prime }\cap A)$

$=P\left(A\right)-P(A\cap B)$

$=0.4-\left(P\right(A)+P(B)-P(A\cup B\left)\right)$

$=0.4-(0.4+0.3-0.5)$

$=0.2$