392.Trapped Behind Five Doors
★★★expected valueCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Jeff is trapped in a room with 5 indistinguishable doors. Two lead to freedom via paths of 2 and 5 miles. Three lead back to the room via paths of 1, 3, and 4 miles, after which the doors are scrambled. What is the expected number of miles Jeff travels before reaching freedom?
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Let be the answer and condition on the first door — returning doors put Jeff back in the same state.
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