Using Expected Value to Buy Car Insurance
Expected value can help you make decisions when the future is uncertain. When you buy car insurance, you need to choose the types of coverage and the amount of coverage that you want. Both of these decisions involve weighing the risks of car accidents and other expenses with the cost of the coverage. Read Lexi’s profile below and answer the questions to help them decide how much liability coverage to purchase.
Lexi is shopping for car insurance; help them decide which level of liability coverage is right for them.
Their state requires at least $20,000 in bodily injury liability insurance.
They commute to work each day in their 2018 Subaru Outback
Each year, they drive approximately 15,000 miles.
The table below shows the estimated probabilities of Lexi being in an accident that causes an injury or fatality over the next year.[1] Use it to answer the following questions.
a. What is P(injury or fatal crash)? Assume the outcomes are mutually exclusive.
b. What is Lexi’s expected value of injury costs for the year, without any insurance?
Lexi can offset some of the risk of these costs by purchasing bodily injury liability coverage. Their state requires at least basic coverage. Use the table of their coverage options to answer the following questions.
a. Lexi looks at the plan options and the probability table. They say “That’s too expensive! I’m not paying at least $25 per month when I have less than a 2% chance of getting in an accident.” What would you say to Lexi?
b. Including insurance premiums, what are Lexi’s expected total bodily injury costs for one year with the basic plan? Hint: Map out the sample space, including how much Lexi would end up paying for each outcome if they had the basic plan. Then, find the expected value.
c. Including insurance premiums, what are Lexi’s expected total bodily injury costs for one year with the moderate plan?
d. Including insurance premiums, what are Lexi’s expected total bodily injury costs for one year with the enhanced plan?