Question

A soccer team is playing in a tournament this weekend. The possible outcomes of a game are win or lose. In the event of a tie at the end of regulation, the teams will play overtime until one team is declared the winner. Assume the outcomes of winning or losing a game are equally likely. The events of winning or losing a game are independent of winning or losing the next game. The team will play up to 3 games in the tournament. Once a team loses they are out of the tournament and will not play any further games.

a) List all the possible outcomes for the team's game results in the tournament.
b) What is the probability that the team will win all three games?
c) What is the probability that the team will win at least one game?

Answer 1

Explanation:

a)

L

W-L

W-W-L

W-W-W

four possibilities.

b) you have 50% chance to win each game

so (1/2)^3 = 1/8 chance to win all three games. 12.5%

c)50%

the latter possibilities don't matter. there is 50% chance you DON'T lose your first game. Therefore you win at least 1 game.