Calculating Insurance Premiums with Variable Damages and Probabilities

[war485]

Homework Statement

Suppose that one year, an insurance company incurred dollar damages,
X, in four different amounts with probabilities, p(x), shown below:

X
0
1000
5000
10000

p(x)
0.7
0.2
0.08
0.02

If the company offers a $500 deductable and wants and wants an
expected profit of $150, how much should it charge for the premium?

Homework Equations

Not even sure what's relevant here. Maybe the expected value is involved somehow:
E(x) = sum ( x*p(x) ) = 800

The Attempt at a Solution

How would I even go about with a problem like this?

 

[Redbelly98]

If the premium is P, what is the company's profit when damages = $0? How about when damages = $1000?

 

[war485]

company's profit is $500 for 0 damage and -$500 profit for 1000 damage.

 

[Redbelly98]

You're not including the premium P, the amount the customer pays for the insurance policy.

First the customer pays the insurance company an amount P. Then later, the company pays back to the customer an amount depending on what the damages are.

 

[war485]

I think I'm getting it.
So overall, if I made up an equation, would this seem right?
Premium = profit + (damages - deductable)
so then my answer should be $800

 

[Redbelly98]

That's right.

(Of course, whenever damages are less than the deductible, no payment is made, but it looks like you realize that.)

 

[war485]

thanks! ^.^