PROBLEM 6E

A life insurance company issues standard, preferred, and ultrapreferred 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 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?

Solution 6E

Step1 of 3:

We have,

Standard policy = S

Preferred policy = T

Ultra preferred policy = U

Dies next year = D

We need to find what are the conditional probabilities of the deceased having had a standard, a preferred, and an ultra preferred policy?

Step2 of 3:

From the given information we have,

Probability of Standard policy P(S) = 60%

= 0.6

Probability of Preferred policy P(T) = 30%

= 0.3

Probability of Ultra preferred policy P(U) = 10%

= 0.1

Similarly,

P(D/S) = 0.01

P(D/T) = 0.008

P(D/U) = 0.007

Now,

We need to find the probability of Dies next year and it is given by

P(D) = P(DS) + P(DT) + P(DU) ………(1)

Where,

1).P(DS) = P(S)P(D/S) [Because P(D/S) = ]

= 0.60.01

= 0.006

Hence, P(DS) = 0.006

2).P(DT) = P(T)P(D/T) [Because P(D/T) = ]

= 0.30.008

= 0.0024

Hence, P(DT) = 0.0024

3).P(DU) = P(U)P(D/U) [Because P(D/U) = ]

= 0.10.007

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