Question

If A and B are events such that P (A) = 0.6, P (B) = 0.3 and P (A ∩ B) = 0.2, find P (A/B) and P (B/A).

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ P\left(A\right)=0.6 \\ P\left(B\right)=0.3 \\ P\left(A\cap B\right)=0.2 \\ \mathrm{Now}, \\ P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)} \\ \Rightarrow P\left(\raisebox{1ex}{$A$}\!\left/ \!\raisebox{-1ex}{$B$}\right.\right)=\frac{0.2}{0.3}=\frac{2}{3} \\ P\left(\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{$A$}\right.\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)} \\ \Rightarrow P\left(\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{$A$}\right.\right)=\frac{0.2}{0.6}=\frac{1}{3} \end{gathered}$$