# When two competing teams are equally matched, the probability that ...

## Transcribed Text

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 your cond usion. Length of series 4 games 5 games 6 games 7 games NBA finals 7 13 22 15 The null hypothesis is that the distribution of length of series follows the probability model consistent with the conjecture that each team has a 50-50 chance of winning each game. For a goodness-of-fit test with 3 degrees of freedom x2 = 1.54 and P = 0.67. 1. Interpret P value within the text 2. Do you reject or not reject null hypothesis? 3. What is your condusion for the problem?

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1.
Under the assumption that the NBA championships has had equally competing teams, the probability of the observed distribution of length of series or the probability of deviation away from the assumption is 67%....

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