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.)
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Solution

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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: Valuesurvive=−188 \text{Value}_{\text{survive}} = -188

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

Step 2: Expected Value Calculation

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

Final Answer

The expected value of the insurance policy for the 31-year-old male is: −8.00 \boxed{-8.00}

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