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

Question #144822
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?
1
Expert's answer
2020-11-18T18:58:41-0500
SolutionSolution

Cost of CD-player = $300\$300

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

Probability of theft is = 0.20.2


\therefore probability of no theft = 10.2=0.81 - 0.2 = 0.8

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

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


So expected return per year

Pi×ri\sum P_i \times r_i where PiP_i is the probability of event(theft or no theft), and is the rir_i return amount


0.8×(20$) + 0.2×$280=$400.8 \times (-20\$)\ +\ 0.2 \times \$280 = \$40

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



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