Q. If $A$ and $B$ are two independent events such that $P\left( A \cap B^{'} \right) = \frac{3}{25}andP(A’ \cap B) = \frac{8}{25}$, then$P(A)$ is equal to
A) $\frac{1}{5}$
B) $\frac{3}{8}$
C) $\frac{2}{5}$
D) $\frac{4}{5}$
Explanation
(a)
Since, events are independent, so
$P\left( A \cap B^{'} \right) = P(A) \times P\left( B^{'} \right) = \frac{3}{25}$
$\Rightarrow P(A) \times \lbrack\left( 1 - P(B) \right\rbrack = \frac{3}{25}$ ...(i)
Similarly, $P(B) \times \left\lbrack 1 - P(A) \right\rbrack = \frac{8}{25}$ ...(ii)
$\therefore$ From Eqs.(i) and (ii), $P(A) = \frac{1}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.