Problem 5. Insurance policy

An insurance company charges its policy holders an annual premium of $400 for the following types of accidents:

• Ifthe policy holder suffers a "major accident" resulting in lengthy hospitalization, the company will payout $40,000 to the injured policy holder.
• If the policy holder suffers a "minor accident" resulting in significant absence from work, the companywill pay out $5,000 to the injured policy holder.
• If no injury is encountered (the most probable event), the company, of course, does not pay out anything to the policy holder.

3

Past records show that, each year, 1 in every 2500 policy holders experiences a "major accident"; and 1 in every 200 experiences a "minor accident". Assume that the only company expense related to this policy is the annualpayout.

1. Construct a probability distribution table for X where X refers to the annual insurance company'sprofit for this policy, where X = Annual Premium-Annual Payout. Keep your work to a minimum of 4 decimals. [6 marks]
2. Compute the expected annual profit that the insurance company can expect to receive per policy holder. [4 marks]