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5. For mathematical modeling, suppose the causes of an accident (A) on a segment of highway can be grouped into speeding (S), tiredness (7), carelessness (C), weather conditions (W), and drunkenness (D). These causes are mutually exclusive and exhaustive. The likelihood of these causes are estimated to be 4:3:1:1:1, respectively. The probabilities of an accident due to S, I, C, W, and D are 0.01, 0.05, 0.01, 0.006, and 0.8, respectively (a) What is the probability of an accident in the segment of the highway? (10 points) (b) If there was an accident, what is the probability that it was caused by drunkenness of the driver? (10 points)