Question

The probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941. If an insurance company sells a one-year, $14,000 life insurance policy to such a person for $455, what is the company's expectation? (Round your answer to two decimal places.)

Answer 1

Given that, Probability that an 80-year-old male I'm the U.S. will die within one year is approximately 0.069941

That is, P(die) = 0.069941

=> P(survive) = 1 - 0.069941 = 0.930059

If 80-year-old man die within one year then insurance company have to pay ($14000 - $455 = $13545) (loss for insurance company is $13545) and if he survive then company gets, $455.

Let X be a profit and loss of insurance company.

X (profit or loss in $)	P(x)
-13545	0.069941
455	0.930059

Then the expected value of X is,

E(X) = (-13545 * 0.069941) + (455 * 0.930059)

=> E(X) = -947.350845 + 423.176845

=> E(X) = -524.174

=> E(X) = -524.17 (rounded to two decimal places)

Therefore, the company's expectation is -$524.17

Note : Another method is,

If old man dies insurance company have to pay $14000 otherwise company will get $455.

Therefore, expected loss/profit for the insurance company is,

(-14000 * 0.069941) + 455 = -979.174 + 455 = -524.174