Question

8) Suppose your team participate in a football tournament in which you play n games. Since you are a very average team, each game is equally likely to be a win, a loss, or a tie. You collect 3 points for each win, 1 point for each tie, and 0 points for each loss. The outcome of each game is independent of the outcome of every other game. Let X be the number of points you earn for game i and let Yequal the total number of points earned over the n games. How many games on average you have to play to reach 30 points?

Answer 1

Each outcome has a probability = 1/3

Expected no of points for 1 game = 1/3 x 3 + 1/3 x 1 + 1/3 x 0 = 4/3

Hence for n games, expected no of points = 4n/3

For 30 points, 4n/3 = 30

Solving n = 30 x 3/4 = 22.5= 23 games (rounding off as n is an integer)