Question

A tree cutting business has an insurance policy to cover any damages caused during the tree cutting process. The business pays an annual premium of $1,500 for a policy that covers up to $500,000 in damages. The probability of a tree causing damage is 0.002. What is the expected value?

Answer 1

-$500

Explanation:

The expected value of a payment from the policy is ...

$500,000 × 0.002 = $1000

Since the business pays $1500 for the policy, the expected value to the business is ...

$1000 - 1500 = -$500 . . . per year

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Of course, the expected value to the insurance company is $500 per year.

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We have computed on the basis of 1 claim per year. If we consider the possibility of multiple independent claims, then the expected payment from the insurance goes up by a factor of 1/(1 -0.002) ≈ 1.002004008016.... This has the effect of increasing the expected value by $2.00 per year to -$498.