Insurance companies use probability and expected value to de

Insurance companies use probability and expected value to determine their rates. Suppose that 200,000 out of 1,000,000 drivers between the ages of 18 and 22 had a car accident. If the average accident cost the insurance company $1,500 and the insurance company charges $800 for an insurance policy, what is the company’s expected profit per policy?

Solution

Proportion of drivers between ages 18 and 22 who had road accident = 200000/1000000 = 0.20

Thus there are two outcomes accident or no accident

P(accident) = 0.20

P(no accident ) = 0.80

Each driver is independent of the other

If accident occurs insurance company has to pay 1500.

Hence cost for insurance company per policy if accident occurs = 1500(0.2) = -300

If no accident premium 800 would be income for insurace company

Hence premium per all policies                                                                         = +800

Hence Expected profit = 800-300 = 500$ per policy