Q. If $P(A) = \frac{1}{12},\ P(B) = \frac{5}{12}$ and $P\left( \frac{B}{A} \right) = \frac{1}{15}$, then $P(A \cup B)$ is equal to
A) $\frac{89}{180}$
B) $\frac{90}{180}$
C) $\frac{91}{180}$
D) $\frac{92}{180}$
Explanation
(a)
$P\left( \frac{B}{A} \right) = \frac{P(A \cap B)}{P(A)}$
$\therefore\ \frac{1}{15} = \frac{P(A \cap B)}{\frac{1}{12}}$
$\Rightarrow \ P(A \cap B) = \frac{1}{180}$
Also, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow \ P(A \cup B) = \frac{1}{12} + \frac{5}{12} - \frac{1}{180} = \frac{89}{180}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.