Question

Brandybuck insurance company (bic) is deciding whether to insure the lives of those leading a quest to moria. based on past experience, the probability of surviving such a quest is 95.2%. if bic charges a premium of 7,901 silver coins and would pay a death benefit of 96,993 silver coins if the insured were to die, what is the expected value of this insurance policy to bic?

Answer 1

The expected value of the insurance policy to Brandybuck Insurance Company is 2,856.088 silver coins, calculated by weighing the probability of policyholders surviving against the probability of them not surviving and the associated financial outcomes of each scenario.

Step-by-step explanation:

To calculate the expected value of the insurance policy to the Brandybuck Insurance Company (BIC), we'd consider two potential outcomes: the policyholder surviving the quest to Moria, and the policyholder not surviving. With the probability of surviving being 95.2% and the probability of not surviving being 4.8% (100% - 95.2%), we can calculate the expected value as follows:

Expected value (EV) = (Probability of Survival) * (Premium) - (Probability of Death) * (Death Benefit)

EV = (0.952 * 7,901 silver coins) - (0.048 * 96,993 silver coins)

EV = 7,511.752 - 4,655.664

EV = 2,856.088 silver coins

Therefore, the expected value of the insurance policy to BIC per insured individual is 2,856.088 silver coins, which means that on average, for each policy sold, BIC would expect to gain 2,856.088 silver coins.