Question

To maintain the spinning wheel game machine, the arcade manager adopts a strategy of emptying the money box (that's where the quarters go after they are inserted in the machine) each time she refills the machine with a new roll of tickets. The ticket refill rolls contain 5000 tickets, and the machine is designed to hold $1300 in quarters in its money box. Assume that the machine was fully loaded with 5000 tickets and had an empty money box when it was first used. Using the manager's maintenance strategy, is there any chance that the money box could become completely full with quarters or overflow with quarters?

How much money would be in the money box?

Answer 1

No. Various arguments can be made, but the central theme is that even if the game returns the minimum of only 1 ticket per play over 5000 plays (extremely unlikely), that represents only 5000 quarters = $1250 which is less than the $1300 capacity. Or from another perspective, the money box can hold 5200 quarters (1300.25=5200), and the most quarters that the machine can earn from a 5000 ticket roll would be 5000 quarters (again, under the extremely unlikely minimal case of 5000 games of 1 ticket each).