Question

If P (A) = 0.4, P (B) = 0.8, P (B/A) = 0.6. Find P (A/B) and P (A ∪ B).

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ P\left(A\right)=0.4 \\ P\left(B\right)=0.8 \\ P\left(B/A\right)=0.6 \\ \mathrm{Now}, \\ P\left(B/A\right)=\frac{P\left(A\cap B\right)}{P\left(A\right)} \\ \Rightarrow 0.6=\frac{P\left(A\cap B\right)}{0.4} \\ \Rightarrow P\left(A\cap B\right)=0.24 \\ P\left(A/B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{0.24}{0.8}=0.3 \\ P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ \Rightarrow P\left(A\cup B\right)=0.4+0.8-0.24=0.96 \end{gathered}$$