Question

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 assuming the prisoner remembers previously chosen doors, and does not re-choose them. Assume the probabilities for the other doors are proportionally larger., what is the expected number of days until the prisoner reaches freedom?

Answer 1

= w corresponding random vaiable Let 4 be door choosen ELE[xly]] E(x) = - ELXly=1] P(4=1) & E[xly=2 & E[+14=3] 914=3) ] ply=2) → Ex: + ) - sex | Ex= 21