easy Probability

Opposite Parity Heads I

A release-checked easy problem for training Conditional Expectation, Coins, Expected Value/LOTUS.

Question

We flip a coin that has a probability $0 < p < 1$ of heads per flip $n \geq 2$ times. Given that the first and last flip are of opposite parity, compute the expected number of heads obtained when $p = 3/4$ and $n = 10$.

Practice focus

This Probability problem is tagged Conditional Expectation, Coins, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.