Question

An insurance company will insure a $50,000 diamond for its full value against theft at a premium of $400 year. Suppose that the probability that the diamond will be stolen is .05, and let x denote the insurance company's profit.

1. Set up the probability of the random variable x.
2. Calculate the insurance company's expected profit.
3. Find the premium that the insurance company should charge if it wants its expected profit to be $1000.00.

Plz show me the each step. I am having hard time finding the profit because the probability that the diamond will be stolen is 0.05

Answer 1

Solution:

Set up the probability of the random variable x.

The random variable has two possible outcomes:

The company losses $49,600 (50000 - 400) if diamond is lost and earns $400 if it is not lost.

x	P(x)

Calculate the insurance company's expected profit.

The expected profit is:

  

Since the expected value is negative, it means the company is expected to lose $2100

Find the premium that the insurance company should charge if it wants its expected profit to be $1000.00.

Answer: We have to find the value of x. We know that:

Therefore, the premium should be $3500 if the company wants its expected profit to be $1000