Jacob is looking to buy some car insurance and is reviewing different policies from several different agencies. The first policy he sees costs$750 for the upcoming year and is worth $10000 if he gets in a collision. After doing some research, he estimates that he has a 8% of getting in acar accident for that year. What is the expected value of buying this insurance policy

The expected value of buying this insurance policy is $50.

The expected value of buying the insurance policy is the weighted average of probabilities of the cost of the insurance and the cover if Jacob gets into an accident.

If Jacob gets into an accident and is covered, his payout will be:

= benefit - cost

= 10,000 - 750

= $9,250

The probability of this happening is 8%.

If Jacob does not get into an accident he would lose the $750 he paid in insurance premiums. The probability of this happening is:

= 100% - 8%

= 92%

The expected value of the insurance is:

= (probability of accident * payout if there is an accident) + (probability of no accident * payout if there is no accident)

= (8% * 9,250) + (92% * -750)

= $50

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