Question

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.

Answer 1

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 $E(X)=P_1X_1+P_2X_2$

      $=0.9996C+0.0004(-250000)$

    

For net gain 500, E(X)=500

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

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

Hence Net gain is 600.4