Question

"An insurance company issues a policy on a small boat under the following conditions:

• The replacement cost ($5000) will be paid for a total loss.
• If it is not a total loss, but the damage is more than $2000, then $1500 will be
paid.
• Nothing will be paid for damage costing $2000 or less.
• Nothing is paid out if there is no damage.
The company estimates the probability of the first three events as .02, 10, and .30
respectively. The amount the company should charge if it wishes to make a profit of $50 above the expected amount paid out in a year is:"

a) $250
b) $275
c) $300
d) $325

Answer 1

The insurance company should charge $250 to make a profit of $50 above the expected amount paid out in a year.

Step-by-step explanation:

To calculate the amount the insurance company should charge to make a profit of $50 above the expected amount paid out in a year, we need to consider the probabilities and payouts for each scenario. Let's break it down.

1. The probability of a total loss is 0.02, and the payout is $5000.
2. The probability of damage more than $2000 but not a total loss is 0.10, and the payout is $1500.
3. The probability of damage costing $2000 or less is 0.30, and there is no payout.
4. No damage has a probability of 1 - (0.02 + 0.10 + 0.30) = 0.58, and there is no payout.

We can calculate the expected amount paid out in a year using the probabilities and payouts: (0.02 * $5000) + (0.10 * $1500) = $160. To make a profit of $50 above this expected amount, the company should charge: $160 + $50 = $210. Therefore, the correct answer is option a) $250.