Questions: There is a 0.9985 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges 188 for insuring that the male will live through the year. If the male 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 31-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 -188. The value corresponding to not surviving the year is 119,812. (Type integers or decimals. Do not round.) b. If the 31-year-old male purchases the policy, what is his expected value? The expected value is (Round to the nearest cent as needed.)

There is a 0.9985 probability that a randomly selected 31-year-old male lives through the year. A life insurance company charges 188 for insuring that the male will live through the year. If the male 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 31-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 -188.
The value corresponding to not surviving the year is 119,812.
(Type integers or decimals. Do not round.)
b. If the 31-year-old male purchases the policy, what is his expected value?

The expected value is
(Round to the nearest cent as needed.)

Transcript text: There is a 0.9985 probability that a randomly selected 31 -year-old male lives through the year. A life insurance company charges $\$ 188$ for insuring that the male will live through the year. If the male 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 31 -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 \$ -188 . The value corresponding to not surviving the year is $\$ 119812$. (Type integers or decimals. Do not round.) b. If the 31-year-old male purchases the policy, what is his expected value? The expected value is $\$$ $\square$ (Round to the nearest cent as needed.)

Solution

Solution Steps

Step 1: Monetary Values for Events

From the perspective of the 31-year-old male, the monetary values corresponding to the two events are calculated as follows:

The value corresponding to surviving the year is given by: \[ \text{Value}_{\text{survive}} = -188 \]
The value corresponding to not surviving the year is given by: \[ \text{Value}_{\text{not survive}} = 120000 - 188 = 119812 \]

Step 2: Expected Value Calculation

To find the expected value $ E $ of the insurance policy, we use the formula: \[ E = \text{Value}_{\text{survive}} \times P(\text{survive}) + \text{Value}_{\text{not survive}} \times P(\text{not survive}) \] Substituting the values: \[ E = -188 \times 0.9985 + 119812 \times 0.0015 \] Calculating this gives: \[ E = -8.0 \]