# Probability and Statistics Question

• Oct 3rd 2007, 05:35 PM
ballinisahobby
Probability and Statistics Question
If anyone can point me in the right direction...
A private pilot wishes to insure his airplane for \$200,000. The insurance company estimates that a total loss may occur with probability of 0.002, a 50% loss with probability 0.01 and a 25% loss with a probability of 0.1. Ignoring other partial losses, what premium should the insurance company charge each year to realize an average profit of \$500?
• Oct 3rd 2007, 05:55 PM
feiyingx
You can start by calculating the Expectation of the amount the insurance will have to pay in the event that something happens to the plane. The answer you get from that expectation is how much the insurance company will "expect" to pay as the cost to insure the plane. Since the insurance company wants to make a \$500 profit on average, then that means the insurance company will have to charge the "expected" cost plus an extra \$500.

If you need more clarifications, let me know. =D
• Oct 3rd 2007, 06:04 PM
ballinisahobby
I need a bit more ok here's another note:
we are going to declare a variable c which represents the amount charged per year and let x represent the net gain to the customer. Here, it is given that e[x] is -\$500.00 and you want to find the value of c such that e[x]-500.00 that is determine how much company should charge so that it will average a profit of \$500 per customer per year.
• Oct 3rd 2007, 06:25 PM
feiyingx
Ok here's how I approached the problem

I broke the insurance company's costs into three scenarios.
Case 1: Total loss. In this case, the insurance company will have to pay the pilot \$200,000 and this happens with a probability of .002

Case 2: 50% loss. In this case, the insurance company will have to pay the pilot 50% of 200,000, which is \$100,000. This happens with a probability of .01

Case 3: 25% loss. Here the insurance company will have to pay the pilot 25% of 200,000, which is \$50,000. This has a probabiilty of .1

Now to find the expectation of the amount the insurance company must pay to cover for the pilot's insurance, we apply the Expectation formula

E[cost] = 200,000*(.002)+100,000(.01)+50,000(.1) = 6400.

This tells you that it costs the insurance company \$6400 to cover for the pilot's airplane. Since the insurance company wants to make a profit of \$500, then they must charge \$6400 to break even with its costs plus an additional charge of \$500 for the extra profit.
Therefore the insurance company will have to charge the pilot \$6900 if the insurance company wants to make a profit of \$500.
• Oct 3rd 2007, 06:30 PM
ballinisahobby
:) wow thanks!!!!!!!!!!!!!!!
i appreciate it so much
• Oct 3rd 2007, 06:36 PM
feiyingx
np =D Glad I can help!