How do you find the probability?

Question

An insurance company issues life insurance policies in 3 separate categories: standard 50%, preferred 40%, and ultra-preferred 10%. Each standard, preferred and ultra-preferred policyholder has probability 0.010, 0.005 and 0.001 of dying in the next year, respectively. What is the probability that a policyholder dies in the next year?

Answer 1

Odds of a standard policy & death: 0.5 * 0.01 = 0.005
Odds of a preferred policy & death: 0.4 * 0.005 = 0.002
Odds of an ultra-preferred policy & death: 0.1 * 0.001 = 0.0001

Add up the three probabilities, and you get 0.0071... or if you prefer the answer as a percentage, 0.71 percent.

Answer 2

Given that each category is mutually exclusive then

P (policy holder dies) = 0.5*0.010 + 0.4*0.005 + 0.1*0.001
= 0.005 + 0.002 + 0.0001
= 0.0071