Accident/Illness Insurance Problem: Some of the highest-paid mathematicians are the

Chapter 9, Problem 8

(choose chapter or problem)

Accident/Illness Insurance Problem: Some of the highest-paid mathematicians are the actuaries, who figure out what you should pay for various types of insurance. Suppose an insurance company has an accident/illness policy that pays $500 if you get ill during any one year, $1000 if you have an accident, and $6000 if you both get ill and have an accident. The premium, or payment, for this policy is $100 per year. One of your friends, who has studied actuarial science, tells you that your probability of becoming ill in any one year is 0.05 and that your probability of having an accident is 0.03. a. Find the probabilities of each event. i. Becoming ill and having an accident ii. Becoming ill and not having an accident iii. Not becoming ill but having an accident iv. Not becoming ill and not having an accident b. What is the mathematical expectation for this policy? c. An insurance policy is actuarially sound if the insurance company is expected to make a profit from it. Based on the probabilities assumed, is this policy actuarially sound?