Question

If Q and R are events such that $P\left(Q\right)=0.8$, $P\left(R\right)=0.5$, $P\left(R/Q\right)=0.4$. Determine the value of $P(Q\cap R)$.

Answer 1

We know,

$P\left(R/Q\right)=\frac{P(R\cap Q)}{P\left(Q\right)}$

$0.4=\frac{P(Q\cap R)}{0.8}$

$P(Q\cap R)=0.4\times 0.8=0.32$