Question

If $P\left(A\right)=0.8,P\left(B\right)=0.5$ and $P\left(\frac{B}{A}\right)=0.4$ find $P(A\cap B)$.

Answer 1

$P\left(A\right)=0.8,P\left(B\right)=0.5$ and $P\left(\frac{B}{A}\right)=0.4$

We know that $P\left(\frac{B}{A}\right)=\frac{P(B\cap A)}{P\left(A\right)}$

$\Rightarrow 0.4=\frac{P(B\cap A)}{0.8}$

$\Rightarrow P(B\cap A)=0.4\times 0.8=0.32$