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Probability : Proportion and Groups

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?

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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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