Question

If P (A) = 0.4, P (B) = 0.3 and P (B/A) = 0.5, find P (A ∩ B) and P (A/B).

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ P\left(A\right)=0.4 \\ P\left(B\right)=0.3 \\ P\left(B/A\right)=0.5 \\ \mathrm{Now}, \\ P\left(B/A\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)} \\ \Rightarrow 0.5=\frac{P\left(A\cap B\right)}{0.4} \\ \Rightarrow P\left(A\cap B\right)=0.2 \\ P\left(A/B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{0.2}{0.3}=\frac{2}{3} \end{gathered}$$