Based on historical data, an insurance company estimates that a particular customer has a 2.4% likelihood of having an accident in the next year, with the average insurance payout being $2700.

If the company charges this customer an annual premium of $250, what is the company's expected value of this insurance policy?

The expected value of this insurance policy is kept at $185.2 based on the historical data provided

Step-by-step explanation:

probability/likelihood of having an accident by the customer is = 2.4% which is 2.4:100 = 0.024 probability:

The cost to the company at 0.024 probability of having an accident

= - $2700 (average insurance payout)

probability of not having an accident by the customer is = 100% - 2.4% = 97.6% which is 97.6 : 100 = 0.976 probability

The cost to the company at 0.976 probability of no accident = $0

The premium paid by the customer annually is = $250

Therefore to get the expected value of the insurance policy (E) will be

(probability of accident) (average insurance payout) + (probability of no accident) (cost of no accident to the company) + premium paid by customer

0.024 (-$2700) + 0.976 ($0) + $250 = $185.2

- $64.8 + $0 + $250 = $185.2