$A$ and $B$ are mutually exclusive and exhaustive, and $P(A) = 2P(B)$. What is $P(A)$?

Explanation

1. 01

   Mutually exclusive and exhaustive: $P(A) + P(B) = 1$.

2. 02

   $2P(B) + P(B) = 1$, so $P(B) = \frac{1}{3}$ and $P(A) = \frac{2}{3}$.