# Strange Tales in Underwriting

An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred.

Of the company’s policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred.

Each standard policyholder has probability 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year.

A policyholder dies in the next year. What is the probability that the deceased policyholder was ultra-preferred?
(A) 0.0001
(B) 0.0010
(C) 0.0071
(D) 0.0141
(E) 0.2817

### 6 guesses to Strange Tales in Underwriting

• iwould say 0.0010

• Dude

Nope, keep trying.

• Geoff

0.0001?

• Dude

Nope, that’s not it.

It’s (D) 0.0141.
10 x 0.001 = 0.01
40 x 0.005 = 0.2
50 x 0.01 = 0.5

Add these together: 0.01 + 0.2 + 0.5 = 0.71
Now divide the ultra-preferred by the total: 0.01/0.71 = 0.01408 or 0.0141

• Dude