Question: 2014 Winter Final - 16

Let $C_1$ be a fair coin that has $H$ on one side and $T$ on the other side. Let $C_2$ be a coin that has $H$ on both sides. We choose one of $C_1$ and $C_2$ uniformly at random and flip it. Define the events

• A = "we choose $C_2$",
• B = "the flip resulted in $H$".

What is the conditional probability $\Pr(A|B)$?