solve this math statistic problem: 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?

Expected loss = ($20000)(0.002) = $40

Expected profit = $300 - $40 = $260

Good

To find the company's expected profit, we need to calculate the profit for each possible outcome and then multiply it by the probability of that particular outcome occurring.

Let's break down the steps:

Step 1: Calculate the potential profit if the collection is stolen.
The insurance company would have to pay the insured value of $20,000. However, they have already collected a premium of $300. So, the profit in this case would be $20,000 - $300 = $19,700.

Step 2: Calculate the potential profit if the collection is not stolen.
In this case, the insurance company would keep the premium of $300 without any payout. So, the profit here would be $300.

Step 3: Calculate the overall expected profit.
We need to multiply the profit for each scenario by its respective probability of occurrence and then sum them up.

Expected profit = (Profit if stolen x Probability of theft) + ( Profit if not stolen x Probability of no theft)
Expected profit = ($19,700 x 0.002) + ($300 x (1-0.002))
Expected profit = $39.4 + $299.4
Expected profit = $338.8

Therefore, the company's expected profit is $338.8.

To calculate the company's expected profit, we need to find the expected value. The expected value is the product of the possible outcomes and their respective probabilities.

Here's how we can calculate the expected profit:

1. Calculate the expected payout:
The company will have to pay the insured amount of $20,000 if the coin collection is stolen. The probability of the collection being stolen is 0.002. So, the expected payout is 20,000 * 0.002 = $40.

2. Calculate the expected premium income:
The company receives an annual premium of $300.

3. Calculate the expected profit:
Expected profit = Expected premium income - Expected payout
Expected profit = $300 - $40 = $260.

Therefore, the expected profit for the insurance company in this case is $260.