19. 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.
Calculate the probability that the deceased policyholder was ultra-preferred.
(A) 0.0001
(B) 0.0010
(C) 0.0071
(D) 0.0141
(E) 0.2817