An insurance company insures ten projects. Each project is independent of the others. In a given year each project has a 5% chance of requiring a $100,000 claim to be paid and a 95% chance of no claim being paid.

a. What is the probability that the insurance company must pay exactly one claim in a given year? (3 point)

b. How much money should be sufficient to cover all claims in a given year with a probability of 95%? Give the smallest $ amount that would suffice.

The insurance company has insured one more project, in addition to the ten projects noted above. This additional project is independent of the other ten. It is riskier and has a 10% chance of requiring a claim to be paid, but the cost of a claim on this project is only $50,000. Answer parts c and d below taking into account that the insurance company now has insured eleven projects.

c. What is the probability that the insurance company pays exactly one claim in a given year? (4 points)

d. The insurance company has to pay exactly one claim in a given year. What is the probability that this claim is for $50,000? (4 points)