The ABC Insurance company charges a 21-year old male a premium of $250 for a one year $100,000 life insurance policy. A 21-year old male has a 0.9985 probability of living for a year (based on data from the National Center for health Statistics.)
A. What is the expected value for a 21-yearold male who buys the insurance?
B. B. What would be the cost of the insurance polity if the company just breaks even?
A. What is the expected value for a 21-yearold male who buys the insurance?
B. B. What would be the cost of the insurance polity if the company just breaks even?
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This is a little morbid but...
This of the two cases, if he lives he will have spent $250 and there's a 99.85% chance of that happening. If he dies he will have gained $99,750 (or I guess someone did) and there's a 0.15% chance of that happening. The expected value is kind of like the weighted average of the two scenarios. Outcome times the probability of that outcome (living) plus the outcome times the probability of that outcome (death). Living (-250)*(0.9985) + Death (99750)*(0.0015) = -249.625 + 149.625 = -100. So his expected outcome is to lose $100.
If they want to only break even that means expected value of $0. So you can set this up as a function with the only unknown being how much he paid.
(-x)(0.9985)+(100000-x)(0.0015) =0
-0.9985x + 150 -0.0015x = 0
-1x = -150
x = 150
So if the insurance cost $150 the man and the insurance company would both break even on average.
This of the two cases, if he lives he will have spent $250 and there's a 99.85% chance of that happening. If he dies he will have gained $99,750 (or I guess someone did) and there's a 0.15% chance of that happening. The expected value is kind of like the weighted average of the two scenarios. Outcome times the probability of that outcome (living) plus the outcome times the probability of that outcome (death). Living (-250)*(0.9985) + Death (99750)*(0.0015) = -249.625 + 149.625 = -100. So his expected outcome is to lose $100.
If they want to only break even that means expected value of $0. So you can set this up as a function with the only unknown being how much he paid.
(-x)(0.9985)+(100000-x)(0.0015) =0
-0.9985x + 150 -0.0015x = 0
-1x = -150
x = 150
So if the insurance cost $150 the man and the insurance company would both break even on average.