Suppose we have two weighted coins, one of which comes up heads with probability 0.1, and the other of which comes up heads with probability 0.8. Unfortunately, the coins are otherwise identical, and we have lost track of which is which. Suppose we flip a randomly chosen coin 14 times and let $N$ be the random variable giving the number of heads seen. If in the first 3 flips we see 2 heads, what is the conditional expected number of heads in the 14 flips?

$E[N|\mbox{2 of first 3 are H}] =$