When two competing teams are equally matched, the probability that each team wins any game is 0

When two competing teams are equally matched, the probability that each team wins any game is 0.5. The (NBA) championship goes to the team that wins four National Basketball Association games

in a best-of-seven series. If the teams were evenly matched, the probability that the final series ends

with one of the teams sweeping four straight games would be 2(0.5)4 =0.125 [team A wins in 4 games

with probability of (0.5)4

; team B can also win in 4 games with the same probability, so the probability

the series ends in 4 games is 2(0.5)4

].

Similarly team A can win in 5 games if team A wins 3 of the first 4 games and then wins game 5. So

team A wins in 5 games with probability 4C3(0.5)3

(0.5)*(0.5)=0.125 . But team B can also win in 5 games

with the same probability, so the probability that the series ends in 5 games is 0.25. Similar probability

calculations show that the probability is 0.3125 that the series lasts six games, and the probability is

0.3125 that the series lasts the full seven games. The table below shows the number of games it took

to decide each of the last 57 NBA champs.

Length of series 4 games 5 games 6 games 7 games

NBA finals 7 13 22 15

Do you think the teams are usually equally matched? Give statistical evidence to support your

conclusion. [30]