The probability that a 22-year-old female in the U.S. will die within one year is approximately 0.00044. If an insurance company sells a one-year, $30,000 life insurance policy to such a person for $295, what is the company's expectation?
To calculate the insurance company's expectation, we need to determine the expected value of the policy.
The company expects to receive $295 from selling the policy, irrespective of whether the person dies or not.
The probability of the person dying within one year is given as 0.00044.
If the person dies, the insurance company will have to pay out $30,000.
Therefore, the expected value for the insurance company can be calculated as:
(Probability of dying * Amount paid out) - (Probability of not dying * Amount received from selling the policy)
= (0.00044 * $30,000) - (0.99956 * $295)
= $13.2 - $294.0682
= -$280.8682
The company's expectation is -$280.8682, indicating that on average, they are expected to lose $280.8682 per policy sold.
To calculate the insurance company's expectation, we need to multiply the potential outcomes by their probabilities and subtract the costs.
1. Calculate the probability of the insured person surviving the year:
P(survive) = 1 - P(die)
P(survive) = 1 - 0.00044 = 0.99956
2. Calculate the probability of the insured person dying:
P(die) = 0.00044
3. Calculate the potential outcomes if the insured person survives:
Outcome(survive) = $0 (since no payout is made)
4. Calculate the potential outcomes if the insured person dies:
Outcome(die) = -$30,000 (insurance payout)
5. Calculate the expected value:
Expectation = (Outcome(survive) * P(survive)) + (Outcome(die) * P(die))
Expectation = (0 * 0.99956) + (-$30,000 * 0.00044)
Expectation = 0 + (-$13.2)
So the insurance company's expectation is -$13.2, indicating they expect to lose an average of $13.2 per policy sold.