Question #195019

A life insurance company will sell a PHP 250,000 one-year term life insurance policy for members of armed forces of the Philippines for the premium of PHP 500. Let X denote the net gain from the insurance company based on the collected data of the company, a member of armed police has a 99.96% chance of surviving within one year. Let X the net gain of an insurance company from a single policy holder.


1
Expert's answer
2021-05-19T17:35:05-0400

Survival probability = 0.9996

Death probability = 1-0.9996=0.0004


Probability Distribution of 'X'-


X: C   PHP 250,000

P: 0.9996   0.0004


Expected E(X)=P1X1+P2X2E(X)=P_1X_1+P_2X_2

      =0.9996C+0.0004(250000)=0.9996C+0.0004(-250000)

    


For net gain 500, E(X)=500


500=0.9996C+0.0004(250000)\Rightarrow 500 =0.9996C+0.0004(-250000)


C=500+1000.9996=6000.9996=600.24\Rightarrow C=\dfrac{500+100}{0.9996}=\dfrac{600}{0.9996}=600.24


Hence Net gain is 600.4

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