Question

Suppose the probability that a basketball team wins each game in a tournament is 60 percent. This probability is constant with each game , and each win/loss is independent. The team plays in the tournament until it loses.

a)Define the random variable and its distribution and find the expected number of games that the team plays.

b)Find the probability that the team plays in at least 4 games.

c)Find the probability that the team wins the tournament if the tournament has 64 teams.

Answer 1

a) here random variable x is number of games played in the tournament until it loses follows geometric distribution

with paramter p=1-0.60 =0.40

henc e expected number of games that the team plays =1/p=1/0.4 =2.5

b)

probability that the team plays in at least 4 games =P(t wins first 3 games) =(0.6)³ =0.216

c)for 64 teams ; a team should win n=6 games to come out as victorious (as 2⁶ =64)

probability that the team wins the tournament if the tournament has 64 teams =(0.6)⁶ =0.0467