Question

If $P\left(A\right)=0.8$ and $P\left(B|A\right)=0.4$, then find $P(A\cap B)$.

Answer 1

Given : $P\left(A\right)=0.8$, $P\left(B|A\right)$

We have the formula $P\left(B|A\right)=\frac{P(A\cap B)}{P\left(A\right)}$

$P(A\cap B)=P\left(B|A\right)P\left(A\right)=0.4\times 0.8=0.32$

Hence, $P(A\cap B)=0.32$