At the town fair, you can pay $5 to toss a ring at a set of bottles. If you get a “ringer” on the small mouth bottle, you win $35. If you get a “ringer” on the medium bottle, you win $10. If you get a “ringer” on the large bottle, you get your $5 fee back (that is, you break even). If you miss, you are out the $5 you paid to play. Joe is a good shot and his probability of getting a ringer on the small, medium, and large bottles is 10%, 10%, and 5%, respectively. The probability distribution of Joe’s winnings (accounting for the $5 that he paid to play) in a single game is given below.
a. What is the math expectation of Joe’s winnings for a single game.
b. What is the math expectation of Joe’s winnings after 5 games.
X | -$5 | $0 | $10 | $35 |
P | 0.75 | 0.10 | 0.10 | 0.05 |
a. What is the math expectation of Joe’s winnings for a single game.
b. What is the math expectation of Joe’s winnings after 5 games.