When Two Competing Teams Are Equally Matched, the Probability That $$2 ( 0.5 ) ^ { 4 } = 0.125 . \text { Further }$$

question 154

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 $$2 ( 0.5 ) ^ { 4 } = 0.125 . \text { Further }$$
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. $$\begin{array} { | l | c | c | c | c | } \hline \text { Length of series } & 4 \text { games } & 5 \text { games } & 6 \text { games } & 7 \text { games } \\\hline \text { NBA finals } & 7 & 13 & 22 & 15 \\\hline\end{array}$$

---

Definitions:

Intellectually Stimulated

The state of being mentally encouraged or energized, often through engagement with challenging and thought-provoking material or activities.

Nature Versus Nurture

A debate regarding the relative importance of an individual's innate qualities versus personal experiences in determining or causing differences in physical and behavioral traits.

Intelligence Tests

Standardized assessments designed to measure human intelligence and cognitive abilities.

DQ Scoring Systems

Evaluation systems used to measure developmental progress or delays in children across various domains.