3. [20 points] A prisoner is trapped in a cell containing 3 doors. The rst 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