Math Corner: Card Shark

By Jason Gershman •

Question: Suppose that the NSU Florida Men’s Baseball team had a promotion whereby students who attend a home baseball game get a sealed trading card of one of 10 different players on the team. Each game attended yields one sealed trading card pack (containing one card) that would have to be opened to reveal its contents. Suppose student Razor Q. Shark attends home baseball games and collects these card packs but does not open any of them (thus not knowing whether he has unique cards or repeats among his collection).

On average, how many baseball games would he need to attend (and therefore how many card packs would he need to collect) to get one complete set of 10 unique cards? (Hint: this is a variation of the classic “Coupon Collector Problem.”)

Show Answer ▼

30 cards packs; you expect to get 10 unique cards in (10/10 + 10/9 + 10/8 + 10/7 + 10/6 + 10/5 + 10/4 + 10/3 + 10/2 +10/1) packs which is approximately 29.3 which you round up to 30.

“Math Corner” is a contest that appears in each issue of The Current and is a collaboration between NSU’s Department of Mathematics | NSU Halmos College of Arts and Sciences | NSU and NSU’s Department of Communication, Media, and the Arts | Halmos College of Arts and Sciences | NSU. Contest submissions to the Math Corner question in the Current’s latest issue can be sent to jgershma@nova.edu up until the date the next issue is published. Prizes are awarded at the end of the academic year.