Question
Marty has been driving his Dad's old beat up car to work and school. To embarrass him, Biff, the local bully, has challenged Marty to
Marty has been driving his Dad's old beat up car to work and school. To embarrass him, Biff, the local bully, has challenged Marty to a race. If he wins, he gets $1,000 but if he loses, he pays $1,000.
Using his Dad's old car, Marty guesses that Biff would win 8 times out of 10. This is embarrassing! To Marty, avoiding the humiliation of not racing Biff at all is worth $100.
Unknown to Biff, Marty's mom, Mrs. McFly, is CFO at Luxury Cars Inc. and she often drives home in the $625,000 company Ferrari. If Marty can secretly borrow his Mom's car, Marty guesses he'll win 9 times out of 10.
There is a catch. Under racing conditions, Marty figures he has a 1% chance of a crash. Using his Dad's car, he'd pay the $500 insurance deductible. Using his Mom's car, he'd do $200,000 in damage, but Luxury Cars Inc. is fully insured so Marty would pay nothing.
Marty needs to consider his options.
Question:
- What is the payoff (please express as positive number) or loss (please express as negative number)of not racing Biff?
- What is the expectedpayoff (please express as positive number) or loss (please express as negative number)of Marty racing using his Dad'scar?
- What is the expected totalpayoff (please express as positive number) or loss (please express as negative number)of racing using his Mom's carincluding anaccident?
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