Question

A city commuter can take one of three possible routes A, B, or C to work. On a given weekday morning, during rush hours, the chances that routes A, B, and C will have traffic congestion, H, are, respectively, 60%, 60%, and 40%. Routes A and B are close by each other such that if the traffic is congested in one route the chance of congestion in the other route increases to 85%. whereas the condition in route C is unaffected (i.e., independent) by the traffic conditions in routes A and B. Also, if the traffic in all the three routes are congested, the chance that the commuter will be late, L, for work is 90%, otherwise it will be 30%. (a) What is the probability that exactly one of the three routes will be congested on a weekday morning? (b) What is the probability that the commuter will be late for work on a given weekday morning? (c) If it is known that the traffic in route A is congested, how would this fact change the probability in (b)?

Note: this problem has already been solved, but I require another solver for assurance.

Answer 1