Expert: Paul Klarreich - 10/13/2009

Question
If a 28 year old pays $207.00 for a one year life insurance policy worth $70K and there is a .9994 probably that he will live through the year, what is the expected value of the insurance policy.  
The answer in the book says -$165.00 but I cannot see how to do this.  Please help ASAP

Answer
Questioner: Nancy
Country: United States
Category: Advanced Math
Private: Yes
Subject: Statistical Question - ASAP
Question: If a 28 year old pays $207.00 for a one year life insurance policy worth $70K and there is a .9994 probably that he will live through the year, what is the expected value of the insurance policy.  
The answer in the book says -$165.00 but I cannot see how to do this.  Please help ASAP
................................................
Hi, Nancy,

Expected value of an event = p(event) * result of event.
Expectation = sum of all expected values.

In this case:

Event:  Death in this year.

p(death) = 0.0006
value of death = 70000.

E.V.(death) = 0.0006 * 70000 = 42

Event:  You survive for this year.
p(life) = .9994
value of life (excuse the expression) = 0.

E.V.(life) = 0.

Sum = 42.

But actually you must subtract the 207 from that:  42 - 207 = -165.