Question

If A and B are two independent events such that P (A ∪ B) = 0.60 and P (A) = 0.2, find P (B).

Answer 1

$$\begin{gathered} P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\right)\times P\left(B\right)\left[\because \mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{independent}\mathrm{events}\right] \\ \Rightarrow 0.6=0.2+P\left(B\right)-0.2\times P\left(B\right) \\ \Rightarrow 0.6-0.2=P\left(B\right)\left(1-0.2\right) \\ \Rightarrow P\left(B\right)=\frac{0.6-0.2}{1-0.2} \\ \Rightarrow P\left(B\right)=\frac{0.4}{0.8} \\ \Rightarrow P\left(B\right)=\frac{1}{2} \\ \Rightarrow P\left(B\right)=0.5 \end{gathered}$$