Question

There is a 0.9986 probability that a randomly selected 33​-year-old male lives through the year. A life insurance company charges ​$182 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$110 comma 000 as a death benefit. Complete parts​ (a) through​ (c) below.

Answer 1

Expected Value = -$42 (loss of 42 dollars)

Explanation:

Complete Question Below:

"There is a 0.9986 probability that a randomly selected 33​-year-old male lives through the year. A life insurance company charges ​$182 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$110 comma 000 as a death benefit. If a 33-year-old male purchases the policy, what is his expected value?"

We can say P(survival) = 0.9986 and thus P(not survival) = 1 - P(survival) = 1-0.9986 = 0.0014

Also,

In case 33 year old doesn't live, the payment would be 100,000 - 182 = $99,818

And

In case 33 year old lives, the payment is

-$182

We know, the expected value is the sum of the product of each possibility with its probability.

`ExpectedValue=\Sigma x*p(x)=(99818)(0.0014)+(-182)(0.9986)=-42`

This means a loss of $42 (or -$42)