His choice of route is independent of the weather. If it rains, the probabilities of arriving late through route A, B and C are0.06, 0.15, 0.12, respectively. The corresponding probabilities if it does not rain are: 0.05, 0.10, 0.15. On the average, one out of every four days is rainy. a) Given that on a sunny day he arrives late, what is the probability that he took rout C? b) If he arrives late on a given day, what's the probability that it is a rainy day? c) How would the knowledge of the probabilities above aid the knowledge engineer in making decisions about which route to take? d) Given that on a sunny day he arrives late, what's the probability that he took route A?