An insurance company insures a person's antique coin collection worth $20,000 for an annual premium of $300. If the company figures that the probability of the collection being stolen is 0.002, what will be the company's expected profit?
Thank you very much--I too finally got this answer.
To calculate the insurance company's expected profit, we need to consider the expected revenue and expected expenses.
Expected Revenue:
The expected revenue is calculated by multiplying the insured amount by the probability of the event occurring. In this case, the insured amount is $20,000 and the probability of the collection being stolen is 0.002.
Expected Revenue = $20,000 * 0.002 = $40
Expected Expenses:
The expected expenses are the sum of the insurance company's costs, which include the claim payouts and the premium collected. In this case, the only expense is the claim payout, as we are not considering any other costs such as administrative expenses.
Expected Expenses = Claim Payout
To find the claim payout, we multiply the insured amount by the probability of the event occurring. Since the insured amount is $20,000 and the probability of the collection being stolen is 0.002, the claim payout is:
Claim Payout = $20,000 * 0.002 = $40
Expected Profit:
The expected profit is calculated by subtracting the expected expenses from the expected revenue.
Expected Profit = Expected Revenue - Expected Expenses
Expected Profit = $40 - $40
Expected Profit = $0
Therefore, the expected profit for the insurance company in this case is $0.