Question

it is estimated that there are 20 deaths for every 10 million people who use airplanes. a company that sells flight insurance provides $100,000 in case of death in a plane crash. a policy can be purchased for $1. calculate the expected value and thereby determine how much the insurance company can make over the long run for each policy that it sells. the expected value is $\square. (round to the nearest cent.)

Explanation:

Step1: Define Probabilities and Outcomes

The probability of death, \( p \), is \( \frac{20}{10000000} = 0.000002 \). The outcome for the insurance company in case of death is \( -\$100000 + \$1 = -\$99999 \) (they pay out $100,000 but receive $1). The outcome in case of no death is \( \$1 \), with probability \( 1 - 0.000002 = 0.999998 \).

Step2: Calculate Expected Value

The expected value \( E \) is calculated as:
\[
E = (-\$99999) \times 0.000002 + \$1 \times 0.999998
\]
First, calculate \( (-\$99999) \times 0.000002 = -\$0.199998 \)
Then, calculate \( \$1 \times 0.999998 = \$0.999998 \)
Add them together: \( -\$0.199998 + \$0.999998 = \$0.8 \)

Answer:

\( 0.80 \)