Chapter 1.5, Problem 6E

A life insurance company issues standard, preferred, and ultra-preferred policies. Of the company’s policyholders of a certain age, 60% have standard policies and a probability of 0.01 of dying in the next year. 30% have preferred policies and a probability of 0.008 of dying in the next year, and 10% have ultra-preferred policies and a probability of 0.007 of dying in the next year. A policyholder of that age dies in the next year. What are the conditional probabilities of the deceased having had a standard, a preferred, and an ultra-preferred policy?