Question

An insurance company is reviewing its policies, and discovers that due to an adminstrative error, it sold a policy for a select life aged 32 to an individual who failed the underwriting. If the probability of a random life aged 32 passing the underwriting is 0.92. What is the probability that this policyholder dies within 5 years from the start of the policy? [Hint: Compare select and ultimate mortality for age 32.]

Answer 1

As we have the mean survival probability is 0.92

and so mean death probability is 1-0.92 = 0.08 and we need to fdetermine the probability of this policy holder dying in 5 years from the start of the policy where the policy holder can technically die at any moment and so it's the problem which can be solved by Poission theorm.

Poisson, is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate.

the formula for the same is

P(x; μ) = (e^-μ) (μ^x) / x!

where μ=0.92 and x<=5

so., The probability that this policyholder dies within 5 years from the start of the policy is

P(X=0)+P(X=1)+P(X=2)+---+P(X=5)  

which is = (e^-0.08) (0.08⁰) / 0! + (e^-0.08) (0.08¹) / 1! + --- + (e^-0.08) (0.08⁵) / 5!

= 0.9996146

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!