Problem 8. Suppose that an insurance company classifies people into low, average and high risk persons. Their records indicate that the probabilities of being involved in an accident over a 1-year period are 0.05, 0.15 and 0.30 for low, average and high risk persons, respectively. Assume that 30% of the population is low-risk, 50% is average-risk and 20% is high-risk.
(a) What proportion of people have accidents in a fixed year?
(b) John Doe had no accidents in 2004, but his wile Jane did. What are he probabilities for each of them to be low-risk persons? Average-risk? High-risk?

Probabilities, proportions and groups are investigated. The solution is detailed and well presented. The solution was given a rating of "5" by the student who originally posted the question.

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