If A and B are two events such that $P(B) = \frac{3}{5},P(A/B) = \frac{1}{2}$ and $P(A \cup B) = \frac{4}{5}$, then $P(A)$ equals to

Here, $P(B) = \frac{3}{5},P(A/B) = \frac{1}{2}$ and $P(A \cup B) = \frac{4}{5}$

$P(A/B) = \frac{{P(A \cap B)}}{{P(B)}}$

$\Rightarrow$ $\frac{1}{2} = \frac{{P(A \cap B)}}{{3/5}}$
$\Rightarrow$ $P(A \cap B) = \frac{3}{5} \times \frac{1}{2} = \frac{3}{{10}}$

and $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\Rightarrow$ $\frac{4}{5} = P(A) + \frac{3}{5} - \frac{3}{{10}}$

$\therefore$ $P(A) = \frac{4}{5} - \frac{3}{5} + \frac{3}{{10}} = \frac{{8 - 6 + 3}}{{10}} = \frac{1}{2}$