Aprisoner 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 .5, .3, and .2, what is the expected number of days until the prisoner reaches freedom?