Answer to Question #144822 in Statistics and Probability for Cameron Foster

Question

Leia is considering insuring against theft the new $300 CD-player she just installed in her automobile.
Her insurance agent tells her that such an option could be added to her present policy for $20 per year.
The agent further states that the probability of theft is 0.2 in a given year. If she takes the insurance,
what is her expected return per year?

Answer 1

$$Solution$$

Cost of CD-player = $\$300$

Cost of additional insurance = $\$20$ per year

Probability of theft is = $0.2$

$\therefore$ probability of no theft = $1 - 0.2 = 0.8$

If there is no theft, then amount paid to insurance is $-\$20$

If there is theft, then amount paid to insurance is $\$300-\$20=\$280$ which is (cost of CD-player recovered - Cost of additional insurance)

So expected return per year

$\sum P_i \times r_i$ where $P_i$ is the probability of event(theft or no theft), and is the $r_i$ return amount

$$0.8 \times (-20\$)\ +\ 0.2 \times \$280 = \$40$$

Hence the expected return per year is $\$40$