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?
To calculate the expected profit for the insurance company, we need to consider the potential outcomes and their probabilities.
The insurance company has two possible outcomes:
1. The collection is stolen: This outcome has a probability of 0.002. In this case, the insurance company would have to pay the insured person the value of the collection, which is $20,000.
2. The collection is not stolen: This outcome has a probability of 1 - 0.002 = 0.998. In this case, the insurance company doesn't have to pay anything.
Let's calculate the expected profit using the formula:
Expected Profit = (Outcome 1 * Probability 1) + (Outcome 2 * Probability 2)
Outcome 1 (collection is stolen) = -$20,000 (as the insurance company has to pay the insured person the value of the collection)
Probability 1 (collection is stolen) = 0.002
Outcome 2 (collection is not stolen) = $0 (as the insurance company doesn't have to pay anything)
Probability 2 (collection is not stolen) = 0.998
Expected Profit = (-$20,000 * 0.002) + ($0 * 0.998)
Expected Profit = -$40 + $0
Expected Profit = -$40
Therefore, the company's expected profit is -$40, meaning they are expected to make a loss of $40.