MATH 131 - Unit 2 Class Activity 2 8/16 Expected value is an important concept to consider when calculating premiums for insurance. The insurance company will assign probabilities to the possible outcomes for the group based on research data. The company will then use expected value to determine the premium to charge. Example 1: Dianne is a 25 year old teacher in good health. Reviewing actuarial tables and based on her age, gender and health, her insurance company has proposed that the probability that she will die this year is 0.001. (a) What is the probability that she will survive the year? (b) If she buys a $100,000 life insurance policy, what are the two possible values the company may pay? (List then in the x column below.) (c) Put the correct P(x) value next to your outcomes. (d) Find the expected value for probability distribution. (e) If the company charges a $100 service fee, what should be Dianne's annual premium? x P( x) x P( x) 1 MATH 131 - Unit 2 Class Activity 2 8/16 Example 2: Dan is pricing car insurance from a new company that only pays out at 3 levels: total, major accident and fender bender. His car is valued at $20,000. After reviewing his application, his insurance company assigned him to a group with the probabilities listed below. These values are used to figure the value the company must charge to cover their payouts. If the company charges a $200 service fee, what will be his annual premium? x , payout P( x) 20,000 total 0.010 10,000 major 0.020 2,000 fender bender 0.090 0 no accident x P( x) ? Try it yourself: If you were buying a similar policy with your car also valued at $20,000, what probabilities for payout do you believe would be assigned. What should be your annual premium? x , payout P( x) 20,000 total 10,000 major 2,000 fender bender 0 no accident 2 x P( x)