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
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.
To calculate the insurance company's expectation, we need to multiply the probability of the event occurring by the amount gained or lost.
In this case, the event is the 80-year-old male dying within one year, and the amount gained or lost is $495 (the cost of the insurance policy).
Expectation = Probability of the event occurring * Amount gained or lost
Expectation = 0.069941 * $495
Expectation ≈ $34.57
Therefore, the insurance company's expectation is approximately $34.57.