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A life insurance company issues standard, preferred, and ultrapreferred policies. Of the
Chapter 1, Problem 1.5-6(choose chapter or problem)
A life insurance company issues standard, preferred, and ultrapreferred policies. Of the companys 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 ultrapreferred 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 ultrapreferred policy?
Questions & Answers
QUESTION:
A life insurance company issues standard, preferred, and ultrapreferred policies. Of the companys 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 ultrapreferred 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 ultrapreferred policy?
ANSWER:Step 1 of 2
Let be the events defined as follows:
Policyholder has a standard policy
Policyholder has a preferred policy
Policyholder has ultra-preferred policy
Policyholder dies next year.
Now,
Also,
To find