Reference no: EM132361831

The highways connecting two resort areas at A and B are shown in Figure above. There is a direct route through the mountains and a more circuitous route going through a third resort area at C in the foothills. Travel between A and B during the winter months is not always possible, the roads sometimes being closed due to snow and ice. Suppose we let E1, E2, and E3 denote the events that highways AB, AC, and BC are passable, respectively, and we know from past years that on a typical winter day, P(E1)= 2/5, P(E2)= 3/4, P(E3)= 2/3 and P(E3|E2)= 4/5, P(E1|E2 ∩ E3)= ½. What is the probability that a traveler will be able to get from A to B?