Q68 / 120 · VITEEE 2007 · Mathematics

If $\mathrm{P}(\mathrm{A})=\frac{1}{12}, \mathrm{P}(\mathrm{B})=\frac{5}{12}$ and $\mathrm{P}(\mathrm{B} / \mathrm{A})=\frac{1}{15}$ then $\mathrm{p}(\mathrm{A} \cup \mathrm{B})$ is equal to

  • Correct answer
    A
    $\frac{89}{180}$
  • B
    $\frac{90}{180}$
  • C
    $\frac{91}{180}$
  • D
    $\frac{92}{180}$

Solution

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, $\begin{array}{l} \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B}) \\ \Rightarrow \mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{1}{12}+\frac{5}{12}-\frac{1}{180}=\frac{89}{180} \end{array}$

Hence, the correct answer is option: 'A'.

Relevant Questions