# Probability - expected number

#53. A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnel that returns him to his cell after 2 days travel. The second leads to a tunnel that returns him to his cell after 4 days travel. The third door leads to freedom after 1 day of travel. If it is assumed that the prisoner will always select doors 1, 2 and 3 with respective probabilities 0.5, 0.3, and 0.2. what is the expected number of days until the prisoner reaches freedom?

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#### Solution Preview

If we assume that X is the time spent on finding the right path and Y is choice of one of those ways then we shall have ...

#### Solution Summary

This shows how to use probabilities to determine the expected number of days until a prisoner reaches freedom.

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