Home » This is a question my professor posed to me: Imagine George. George has $10,000 in cash, and a car worth $30,000. George is considering insurance. He…

This is a question my professor posed to me: Imagine George. George has $10,000 in cash, and a car worth $30,000. George is considering insurance. He…

This is a question my professor posed to me:

Imagine George. George has $10,000 in cash, and a car worth $30,000. George is considering insurance. He can choose between the following three options:

Full insurance, which covers the cost of his car being stolen or in an accident costs $5,000

Insurance against theft, which covers losses due to theft, but not accident, costs $3,500

If George does not buy any insurance, in addition to the risk of theft and accidents, he also exposes himself to being fined if stopped by police without insurance.

The risk of theft is 5%, the risk of accident is 5%, and the risk of being stopped is 10%.

If his car is stolen or in an accident it looses all value. If he is fined for not having insurance he looses $20,000.

  1. What is the expected value for George if he were to get full insurance?
  2. What is the expected value for George if he were to get insurance against theft?
  3. What is the expected value for George if he were to get no insurance at all?

So I’m pretty much stuck on all of them because I’m confused about calculating expected value. I’ll try to explain my thought process so far.

For 1, I got -5000. My formula was [0.05 x (-30000)] + [0.05 x (-30000)] + [.1 x (-20000)] = -5000.

Basically, the (chance of theft * value lost from car) + (chance of accident * value lost from car) + (chance of being stopped * $20000 fine).

Am I right in my calculation for the first part? I haven’t been able to start the other 2 problems yet because I’m not sure if I’m even right for the first part.

Anyways, any help or clarity would be much appreciated! Thanks a lot.

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