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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

603.0. "world series probability" by RAYNAL::OSMAN (and silos to fill before I feep, and silos to fill before I feep) Mon Oct 27 1986 13:20

Consider a sporting event, such as the world series, in which the
first team to win 4 games is the champion.

Suppose the teams are of equal strength.  What is the probability
that the match lasts 7 games ?

How about the general question:  One team has a probability of P
of winning any given game.  What is the probability, M (stands for "max"),
that a "best of L" series runs the full L games ?

/Eric

T.R	Title	User	Date	Lines
603.1	6-game series is much more common	MODEL::YARBROUGH	`Mon Oct 27 1986 14:03`	7
	>Suppose the teams are of equal strength. What is the probability >that the match lasts 7 games ? The series will go to 7 games only if the first 6 are split 3-3, which will happen 6!/(3!*3!)/2^6 = 5/16 of the time. A six-game series will happen 30/64 of the time.
603.2	6 and 7 games are equally likely	VINO::JMUNZER	`Mon Oct 27 1986 15:40`	14
	For either a six or seven game series, the first five games must be split 3 - 2. then there are equal chances of 4 - 2 (six game series) and 3 - 3 (seven game series). But the formula of .1 looks good: 2n ( ) x p ^ n x (1 - p) ^ n n John
603.3	307 echoes	VINO::JMUNZER	`Mon Dec 29 1986 19:25`	6
	What fraction of those World Series in which the American League didn't get shut out should have lasted seven games? (Assuming even chances of winning for all teams in all Series.) John
603.4	another look	ESTORE::ROOS	`Thu Jan 15 1987 16:08`	19
	refering to .1 The probability that the series will end in exactly 6 games (assuming equal strength) is 5/16. As a matter of fact, the following is true: Number of games Probability ================= ============= 4 2/16 5 4/16 6 5/16 7 5/16 Also, the expected number of games is 5 and 13/16.
603.5	exit	CIVAGE::BUCHANAN	`Tue Jul 23 1991 22:57`	5
	s'pose that the two teams aren't equally matched? How does the probability of a 6-game tournament vary? A 5-game tournament? What would your intuition say? Andrew.