Hello, I am bugfree Assistant. Feel free to ask me for any question related to this problem
To determine the probability that a best-of-7 series between two evenly matched teams goes to a decisive 7th game, we need to consider the conditions required for the series to reach this point. Specifically, both teams must win exactly 3 games each in the first 6 games.
Understanding the Problem:
Mathematical Representation:
Binomial Probability Formula:
The probability of a specific sequence of wins can be calculated using the binomial probability formula:
P(x wins)=(xn)⋅px⋅(1−p)n−x
Where:
Calculate Combinations:
(36)=3!(6−3)!6!=3×2×16×5×4=20
Calculate Probability:
P(3 wins for each team)=(36)⋅(0.5)3⋅(0.5)3
P(3 wins for each team)=20×(0.5)6=20×641=6420=165
Final Result:
Why Binomial Distribution?
Why 165?
This approach provides a comprehensive understanding of how to calculate the probability of a 7-game series in a competitive environment with evenly matched teams.