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Answer:
The expected number of days until prisoner reaches freedom is 12 days
Step-by-step explanation:
From the given information:
Let X be the random variable that denotes the number of days until the prisoner reaches freedom.
We can evaluate E(X) by calculating the doors selected, If Y be the event that the prisoner selects a door, Then;
E(X) = E( E[X|Y] )
E(X) = E [X|Y =1 ] P{Y =1} + E [X|Y =2 ] P{Y =2} + E [X|Y =3 ] P{Y =3}
Solving for E[X]; we get
E[X] = 12