Question

Suppose that the typical male driver in a brand new car has a 5% chance of causing a collision that totals their car each year, while the typical female driver in a brand new car has a 1% chance of causing a car-ending collision each year. Assuming that men and women buy on average the same cost new car at a price of $33,000, how much more should we expect men driving new cars to pay for auto insurance annually compared to women (driving new cars, that is)? (Assume fancy-pants full auto insurance--no deductible!)

Answer 1

Expected Payoff by the insurance company in case of collision by a male driver = $33,000*0.05 = $1650.

Expected Payoff by the insurance company in case of collision by a female driver = $33,000*0.01 = $330.

If insurance premium is Actuarially fair, then Premium paid by a male driver = $1650 and Premium paid by a female driver = $330. Hence the premium paid by a male driver is $1320 more. Or the premium paid by a male driver is 5 times the premium paid by a female driver.