Let X be the damage incurred in in a certain type of accide

Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.85, 0.10, 0.03, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge? Show your work.

Solution

Solution:

With the $500 deductible policy, the company\'s expected out outlay is:

0.85 * 0 + 0.10 * (1000-500) + 0.03 * (5000-500) + 0.02 * (10000-500)

= $375

Premium amount company should charge = $375 + $100 = $475 Answer