A car owner must decide whether she should take out a $100-deductible collision policy in addition to her liability insurance policy. Records show that each year, in her area, 17% of the drivers have an accident that is their fault or for which no fault is assigned, and that the average cost of repairs for these types of accidents is $1200. If the $100-deductible collision policy costs $100 per year, would she save money in the long run by buying the insurance or "taking the chance"? (Hint: Find the expected values if she has the policy and if she doesn't have the policy and compare them.)
A)by buying the insurance
B)by taking the chance

Question

A car owner must decide whether she should take out a $100-deductible collision policy in addition to her liability insurance policy. Records show that each year, in her area, 17% of the drivers have an accident that is their fault or for which no fault is assigned, and that the average cost of repairs for these types of accidents is $1200. If the $100-deductible collision policy costs $100 per year, would she save money in the long run by buying the insurance or "taking the chance"? (Hint: Find the expected values if she has the policy and if she doesn't have the policy and compare them.) ​
A)by buying the insurance
B)by taking the chance

Quizplus · Accepted Answer

If the car owner takes out the $100-deductible collision policy:

Expected cost = (0.17)(1200-100) + (0.83)(0) + 100 = $191.00

If the car owner doesn't take out the policy:

Expected cost = (0.17)(1200) + (0.83)(0) = $204.00

Therefore, the car owner would save money in the long run by buying the insurance because the expected cost is lower with the policy ($191.00 < $204.00).

A Car Owner Must Decide Whether She Should Take Out