A release-checked easy problem for training Expected Value.
Question
A farmer wants one male and one female goat for breeding. He goes to Mount Everest to find goats. Each goat is known to be male with probability $\dfrac{3}{4}$, independent of all other goats. The farmer takes a goat, examines it, and then leaves with the first two goats that are of opposite genders. If $N$ is the total number of goats that the farmer examines until he observes two goats of opposite genders, find $\mathbb{E}[N]$.
Practice focus
This Probability problem is tagged Expected Value. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.