Question

A company sells an insurance policy against losses incurred during travel for $15. 40,000 customers buy the insurance policy. The policy pays the full amount claimed up till $5,000. Most policy holders claim nothing, the rest either $500 or $5,000. Each customer has the following probabilities of claiming a certain amount for damages, independent of the other customers.

Claim $0 $500 $5,000
Probability 99% 0.8% 0.2%
Estimate the probability that the company makes a positive net profit across the 40,000 contracts.

Answer 1

To estimate the probability of the company making a positive net profit across the 40,000 contracts, we calculate the expected claims and premiums collected. The probability is 1.

Step-by-step explanation:

To estimate the probability that the company makes a positive net profit across the 40,000 contracts, we need to consider the expected claims and premiums collected.

For each customer, the expected claim can be calculated by multiplying the claim amount by the probability of that claim amount occurring. The expected claim for $0 is $0, for $500 is $4, and for $5,000 is $10.

The total expected claims for all customers is then $0 + (40,000 x $4) + (40,000 x $10) = $400,000.

The premiums collected is calculated by multiplying the number of customers by the premium amount. The total premiums collected is $15 x 40,000 = $600,000.

The probability of the company making a positive net profit is the probability that the total premiums collected is greater than the total expected claims. In this case, the probability is the probability that $600,000 is greater than $400,000, which is 1.