$A$ and $B$ are independent, $P(A \cap B) = 0.12$ and $P(A' \cap B) = 0.28$. What is $P(A)$?

Explanation

1. 01

   $B$ splits into $A \cap B$ and $A' \cap B$: $P(B) = 0.12 + 0.28 = 0.4$.

2. 02

   By independence, $P(A) = \frac{P(A \cap B)}{P(B)} = \frac{0.12}{0.4} = 0.3$.