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Suppose an automobile insurance company classifies a driver as good, average, or bad. Of all their...

Suppose an automobile insurance company classifies a driver as good, average, or bad. Of all their insured drivers, 5.72% are classified good, 54.77% are average, and the rest are classified as bad. Suppose for the coming year, a good driver has a 5.32% chance of having an accident, and average driver has 13.39% chance of having an accident, and a bad driver has a 40.90% chance. What is the probability of a driver NOT having an accident in the coming year?

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Answer #1

P(Accident)

= P(Accident | Good Driver)*P(Good Driver) + P(Accident | Average Driver)*P(Average Driver) + P(Accident | Bad Driver)*P(Bad Driver)

= 0.0532*0.0572 + 0.1339*0.5477 + 0.4090*(1 - 0.0572 - 0.5477)

= 0.2380

Hence,

P(Not having an accident) = 1 - 0.2380 = 0.7620

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