# Binomial Distribution, I think HELP!!!

#### Tflipp

##### New Member
I have a problem that states:
An insurance company will insure a $75,000 Hummer for its full value against theft at a permium of$1,500 per year. Suppose that the probability that the Hummer will be stoln is .0075.

1. Calculate the insurance company's expected net profit
2. Find the premium that the insurance company should charge if it wants its expected net profit to be $2000. I calculated #1 to be$926.25 (is this correct?)
I can't seem to figure out how to structure question 2 in order to get an answer.

Thanks for the help!

#### F.A.P

##### New Member
If the car has an infinite lifelength an the probability that tha car is stolen is 0.0075 per year, you could approach it as follows:

Let Y be the year the car is stolen. Y is then FirstSuccess(0.0075) with pmf

P(Y = n) = (1 - p)^(n-1)*p, n = 1,2,....

Let X be the net profit of the insurance company. Given the year n the car is stolen we have

E(X|Y=n) = n*1500 - 75000

Now use "law of total expectation" to find (1). The solution to (2) follows quite naturally from the work in (1).