A release-checked easy problem for training Expected Value.
Question
Suppose we want to simulate an event with probability $\dfrac{1}{3}$. This is possible via the following scheme: Flip a fair coin twice. If the outcome is HH, we say the event happened. If the outcome is HT or TH, we say that the event did not happen. If the outcome is TT, we re-run the 2 flips experiment under the same rules. Find the expected amount of coin flips needed to simulate this event.
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.