His choice of route is independent of the weather. If it rains, the probabilitie

Question

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?

Explanation / Answer

(P(C|P_{no ; rain}) = P(C)intersect P_{no ; rain}/P_{no_rain} = 0.15)... exclusive events! (1 - (0.05 + 0.10 + 0.15)/(0.05 + 0.10 + 0.15+ 0.06+0.15+0.12) = 11/21) If it rains/is a sunny day, he takes the route that has the least total probability to be late. 0.06

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