Question

A 20-year-old woman takes out a $12,000 one-year life insurance policy that costs $110. Mortality tables indicate that the probability that a 20-year-old women will die within a year is 0.006. (Note: the policy is for one year) Fill in the values for a probability model for the company’s profit on a 20-year-old woman’s policy.

Outcome x    P(X=x)

She lives the whole year

She dies within the year 0.006

Answer 1

P(She lives the whole year) + P(She dies within the year) = Total probability

Therefore, P(She lives the whole year) = Total probability - P(She dies within the year) = 1 - 0.006 = 0.994

X = company's profit = $110 if She lives the whole year

and X = company's profit = 110 - 12000 = -11890 dollar if She dies within the year

So the  probability model for the company’s profit on a 20-year-old woman’s policy is as follows:

Outcome	x	P(X=x)
She lives the whole year	110	0.994
She dies within the year	-11890	0.006

So,