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:

Logarithm

The exponent to which a base, typically 10 or e, must be raised to produce a given number.

Properties of Logarithms

The set of rules that apply to logarithmic functions, including product, quotient, and power rules.

Logarithm

The exponent or power to which a base must be raised to produce a given number, commonly used in the operations of multiplication and division in a compressed form.

Change-of-Base Formula

A formula that allows the base of a logarithm to be changed, facilitating easier calculation.