Suppose that a car rental agency offers insurance for a week that will cost $10

Question

Suppose that a car rental agency offers insurance for a week that will cost $10 per day. A minor fender bender will cost $1,500, while a major accident might cost $15,000. Without the insurance, you would be personally liable for any damages. What should you do? Clearly, there are two decision alternatives: take the insurance, or do not take the insurance. The uncertain consequences or events that might occur, are that you would not be involved in an accident that you would be involved in a fender bender, or that you would be involved in a major accident. Develop a payoff table for this situation. What decision should you make using each strategy?

Average payoff strategy:

Aggressive strategy:

Conservative strategy:

Opportunity loss strategy:

Explanation / Answer

Assume that you researched insurance industry statistics and found out that the probability of major accident is 0.05%, and that the probability of a fender bender is 0.16%. What is the expected value decision? Would you choose this? Why or why not? What would be some alternate ways to evaluate risk?
The car rental agency offers insurance at $10/day for a week, which is 7 days, which equals $70/week (10*7=70). To calculate the expected value decision, we can add the product of probabilities and involved costs.
To find the expected value of decision to take the insurance we do the following calculations:
0.05/100*15,000 + 0.16/100*1,500 + (1-0.05/100-0.16/100)*(-70) = $-59.95
To find the expected value of decision to not take the insurance we do the following calculations:
0.05/100*(-15,000) + 0.16/100*(-1,500) + (1-0.05/100-0.16/100)*70 = $59.95

We should not take the insurance because the expected value of decision to not take the insurance is greater than the expected value of decision to take the insurance.

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