Problem
of the
Week

PROBLEM 202

This problem is in honor of the Dr. Tony Bedenikovic, the mathematics' department number one St. Louis Cardinals fan.

The National League Baseball Series ended last Thursday night with a come-from-behind victory by the St. Louis Cardinals over the Houston Astros.   The series is a best-of-seven format, where the first team to win four of seven games is the champion.  After the first six games the series was tied at three games apiece.  What is the probability of that happening?  

More precisely, assume that two evenly matched teams play each other in a best-of-seven series.  What is the probability that all seven games have to be played before the series is decided?

For the real sluggers: What is the probability of the series going to seven games if the teams are not equally matched, having instead probability p and 1-p of winning each game?

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ã2004 Alberto L. Delgado