A life insurance company issues standard, preferred, and ultrapreferred policies. Of the company’s policyholders of a certain age, 60and 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?

a) The conditional probability of the deceased having had a standard policy = 0.6593

b) The conditional probability of the deceased having had a preferred policy = 0.2637

c) The conditional probability of the deceased having had an ultra preferred policy = 0.0769

Step-by-step explanation:

We are given that a life insurance company issues standard, preferred, and ultra preferred policies to it's policyholders.

Let Proportion of Policyholders having standard policies, P() = 0.6

     Proportion of Policyholders having preferred policies, P() = 0.3

     Proportion of Policyholders having ultra preferred policies, P() = 0.1

Now, D = event of policyholder dying next year

So, Probability of policyholder dying given he had standard policies,

      P(D/) = 0.01.

Probability of policyholder dying given he had preferred policies, P(D/) =

 0.008.

Probability of policyholder dying given he had ultra preferred policies,

P(D/) = 0.007.

Now using Bayes' Theorem we will find the required conditional probability;

The formula is given by, P(/D) = ,where i goes from 1 to 3.

a) Probability of the deceased having had a standard policy given he died in the next year = P(/D)

   P(/D) =

                = = = 0.6593 .

b) Probability of the deceased having had a preferred policy given he died in the next year = P(/D)

    P(/D) =

                 = = = 0.2637 .

c) Probability of the deceased having had a ultra preferred policy given he died in the next year = P(/D)

     P(/D) =

                  = = = 0.0769 .

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.