$P(A \mid B) = \frac{1}{2}$, $P(B \mid A) = \frac{2}{3}$ and $P(A \cap B) = \frac{1}{6}$. What is $P(A \cup B)$?

Explanation

1. 01

   $P(B) = \frac{P(A \cap B)}{P(A \mid B)} = \frac{1/6}{1/2} = \frac{1}{3}$ and $P(A) = \frac{P(A \cap B)}{P(B \mid A)} = \frac{1/6}{2/3} = \frac{1}{4}$.

2. 02

   $P(A \cup B) = \frac{1}{4} + \frac{1}{3} - \frac{1}{6} = \frac{5}{12}$.