Question

Erik Red is a player for the Arizona Snowflakes in the National Foosball League. The league has 27 teams, each with 75 players. Every week, 10 players per team are chosen for random drug testing. Let Y be the number of players who are chosen for random drug testing at least 4 times in the first 9 weeks of the foosball season. What is the maximum possible value of Y, i.e., the largest k such that P(Y=k) > 0?

Answer 1

27 teams*10 players =270 players per week

Number of players for 9 weeks =270*9 =2,430 players (However, total players available =27*75 =2,025)

Since each player is tested at least 4 times (at least 4 means 4, 5, 6,7,....), maximum possible number of players =2,430/4 =607.5

(And if we divide by 5, it will be less than 607.5. If we divide by 6, it will be even less and so on).

Since, the number of players cannot be a fraction, round it to 608.

Thus, the largest k such that P(Y=k) > 0 is 608.