When Two Competing Teams Are Equally Matched, the Probability That

question 54

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

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Definitions:

Maturity Stage

A phase in the life cycle of a product, business, or industry where growth stabilizes, and sales plateau, often leading to increased competition for market share.

Business Incubators

Entities structured to boost the development and prosperity of start-up businesses by offering a variety of business support tools and services.

Survival Rates

The percentage of individuals or entities that continue to exist after a certain period of time or through specific challenges.

Start-Ups

Newly established businesses often characterized by innovation and aimed at fulfilling a specific market need or niche.