When Two Competing Teams Are Equally Matched, the Probability That

question 39

Essay

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 games in a
best-of-seven series. If the teams were equally 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. Further probability calculations indicate that 25% of these series should last five games, 31.25% should last six games, and the other 31.25% should last the full seven games. The table shows the number of games it took to decide each of the last 57 NBA champs. Do you think the teams are usually equally matched? Give statistical evidence to support yourconclusion.

$\begin{array}{|l|c|c|c|c|}\hline\text { Length of series }& \text {4 games} & \text {5 games} &\text { 6 games} &\text { 7 games} \\\hline\text { NBA finals }& 7 & 13 & 22 & 15 \\\hline\end{array}$

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