easy Probability
A release-checked easy problem for training Conditional Expectation.
Lewis is trapped in a room with $4$ doors. He selects a door uniformly at random. Two of the doors have paths of lengths $5$ and $7$ miles that lead to freedom. The other two doors have paths of lengths $2$ and $4$ miles that lead back to the room Lewis is currently in. If Lewis selects a door uniformly at random in each step, find the expected amount of miles that he travels before reaching freedom?
This Probability problem is tagged Conditional Expectation. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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