Probablity #2

[REL18]

A risk of rowing single scull boats is that striking a submerged rock may puncture the hull. Rowers with different levels of experience have different propensities to have this sort of accident. Assume that you’re a member of a rowing club consisting of 100 experienced rowers, 100 intermediate rowers and 100 ‘beginner’ rowers (but the club management do not know which rowers have which levels of experience). Over the past five years, on average 10 of the ‘beginner’ rowers, 6 of the intermediate rowers and 4 of the experienced boaters have serious submerged-rock accidents each year. Mending a scull hull costs $500.

Someone proposes that the club offer an extra membership benefit to members willing to pay for it: under the benefit scheme, the club would pay the costs of hull repair for submerged-rock punctures.

A. What advantage would this proposal have compared to letting people pay for their own hull repairs?
B. If the management could force all members to join the benefit scheme, how much would they charge per person (based on the historic data) in order to cover the total costs of the scheme? [5 points] If the scheme was offered at this price, would it be likely to cover costs? Why or why not?
C. If the benefit scheme is optional, so that members can choose to join or not join, but the management still wants the total charges to cover the total costs, would they have to charge each person more or less (based on historical data)? Explain your answer and estimate the new charge.