Mathematics - Application of Derivative Question with Solution | TestHub

Given $\mathrm{P}(\mathrm{A})=\frac{1}{12},\mathrm{P}(\mathrm{B})=\frac{5}{12},\mathrm{P}(\mathrm{B}/\mathrm{A})=\frac{1}{15}$ We know that $P(B/A)=\frac{P(A\cap B)}{P(A)}$ $\begin{array}{l}\Rightarrow \frac{1}{15}=\frac{\mathrm{P}(\mathrm{A}\cap \mathrm{B})}{1/12}\\ \Rightarrow \mathrm{P}(\mathrm{A}\cap \mathrm{B})=\frac{1}{15\times 12}=\frac{1}{180}\end{array}$ But, $\begin{array}{l}\mathrm{P}(\mathrm{A}\cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A}\cap \mathrm{B})\\ \Rightarrow \mathrm{P}(\mathrm{A}\cup \mathrm{B})=\frac{1}{12}+\frac{5}{12}-\frac{1}{180}=\frac{89}{180}\end{array}$