Question

the probability that an 80 year old male in the united states will die within one year is approximately 0.069941. if an insurance company sells a one year $10,000 life insurance policy to such a person for $495 what is the company’s expectation

Answer 1

To find the company's expectation (or expected value), we multiply the potential outcomes by their respective probabilities and sum them up.

Let's break down the expected value calculation step by step:

1. If the insured person dies within one year, the insurance company pays out $10,000.
2. If the insured person survives one year, the insurance company keeps the $495 premium paid by the customer.

Now, let's calculate the expected value:

Probability of death: 0.069941
Payout in case of death: $10,000

Expected payout in case of death: 0.069941 * $10,000 = $699.41

Probability of survival: 1 - 0.069941 = 0.930059
Payout in case of survival: $495 (the premium paid by the customer)

Expected payout in case of survival: 0.930059 * $495 = $459.97

Overall expectation: $699.41 + $459.97 = $1,159.38

Therefore, the company's expectation (or expected value) is $1,159.38.