A box contains 5 coins and each has a different probability of showing heads. Let $p_1, p_2, p_3, p_4, p_5$ denote the probability of heads on each coin.
Suppose that $p_1 = 0, p_2 = 1/4, p_3 = 1/2, p_4 = 3/4$ and $p_5 = 1$. Select a coin at random and toss it. Suppose a head is obtained. Toss the coin again. What is the probability of another head. In other words, find $P(H_2 | H_1)$, where $H_j$ denotes "heads on toss j".
The progress I have been able to make is to compute the probability $P(H_1)$ using total probability theorem, but I don't know how to compute $P(H_2 \cap H_1)$.