Question

In: Statistics and Probability

An auto insurance company classifies its policyholders as low, average, or high risks: 30% are deemed...

An auto insurance company classifies its policyholders as low, average, or high risks: 30% are deemed low risks, 50% are deemed average risks, and 20% are deemed high risks. Historical data suggested that 5% of low risks, 10% of average risks, and 40% of high risks will be involved in an accident in the coming year. (a) What is the probability that a randomly selected customer files an accident claim in the coming year? (b) An accident claim has just been filed with the company. What is the probability that this customer was classified as a low risk? An average risk? A high risk?

Expert Solution

P(low risk) = 0.3

P(average risk) = 0.5

P(high risk) = 0.2

P(accident claim | low risk) = 0.05

P(accident claim | average risk) = 0.1

P(accident claim | high risk) = 0.4

a) P(accident claim) = P(accident claim | low risk) * P(low risk) + P(accident claim | average risk) * P(average risk) + P(accident claim | high risk) * P(high risk)

= 0.05 * 0.3 + 0.1 * 0.5 + 0.4 * 0.2

= 0.145

b) P(low risk | accident claim) = P(accident claim | low risk) * P(low risk) / P(accident claim)

= 0.05 * 0.3 / 0.145

= 0.103

P(average risk | accident claim) = P(accident claim | average risk) * P(average risk) / P(accident claim)

= 0.1 * 0.5 / 0.145

= 0.345

P(high risk | accident claim) = P(accident claim | high risk) * P(high risk) / P(accident claim)

= 0.4 * 0.2 / 0.145

= 0.552

orchestra answered 2 years ago

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