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.
