$A$ and $B$ are independent, $P(A) = \frac{1}{2}$ and $P(A \cup B) = \frac{3}{5}$. What is $P(B)$?

Explanation

1. 01

   $P(A \cup B) = P(A) + P(B) - P(A)P(B)$: $\frac{3}{5} = \frac{1}{2} + p - \frac{p}{2}$.

2. 02

   $\frac{p}{2} = \frac{1}{10}$, so $p = \frac{1}{5}$.