$P(E) = 0.4$, $P(A \mid E) = 0.5$ and $P(A \mid E') = 0.2$. What is $P(E \mid A)$?

Explanation

1. 01

   $P(A) = 0.4 \times 0.5 + 0.6 \times 0.2 = 0.2 + 0.12 = 0.32$.

2. 02

   $P(E \mid A) = \frac{0.2}{0.32} = 0.625$.