Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel which returns him to his cell after two days travel. the second door leads to a tunnel that returns him to his cell after three days travel. the third door leads immediately to freedom.
(a) assuming the prisoner will always select doors 1, 2 and 3 with probabilities 0.5, 0.3 and 0.2 respectively, what is the expected number of days until he reaches freedom?
(b) calculate the variance of the number of days until the prisoner reaches freedom.