does not survive the year, the policy pays out $\$ 120,000$ as a death benefit. Complete parts (a) through (c) below.
a. From the perspective of the 30 -year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
The value corresponding to surviving the year is $\$-199$.
The value corresponding to not surviving the year is $\$ 119801$.
(Type integers or decimals. Do not round.)
b. If the 30 -year-old male purchases the policy, what is his expected value?
The expected value is
(Round to the nearest cent as needed.)
Answer
Final Answer: The expected value of the insurance policy for a 30-year-old male, given the assumptions we made, is \(\boxed{-\$79}\).
Step 1 ：The problem is asking for the expected value of an insurance policy for a 30-year-old male. The expected value is calculated by multiplying each possible outcome by their probability, and then summing these values.
Step 2 ：There are two possible outcomes: surviving the year and not surviving the year. The monetary value corresponding to surviving the year is \(-\$199\) (the cost of the policy), and the value corresponding to not surviving the year is \(\$119,801\) (the payout of the policy minus the cost).
Step 3 ：However, the problem does not provide the probabilities of these outcomes. Without this information, we cannot calculate the expected value. Therefore, we need to make an assumption or obtain the missing information to proceed.
Step 4 ：For example, we could assume that the probability of a 30-year-old male surviving the year is 0.999 (based on actuarial tables), and the probability of not surviving is 0.001.
Step 5 ：With these assumptions, we can calculate the expected value as follows: Expected Value = \((0.999 * -\$199) + (0.001 * \$119,801)\)
Step 6 ：The expected value of the insurance policy for a 30-year-old male, given the assumptions we made, is approximately \(-\$79\). This means that, on average, a 30-year-old male would lose about \(\$79\) by purchasing this insurance policy.
Step 7 ：However, this is a simplification and the actual expected value could be different depending on the exact probabilities of surviving and not surviving the year.
Step 8 ：Final Answer: The expected value of the insurance policy for a 30-year-old male, given the assumptions we made, is \(\boxed{-\$79}\).
