# (Simple) World series probability question?

• Mar 13th 2011, 04:10 PM
jellyksong
(Simple) World series probability question?
In the World Series, two teams play each other until one team wins 4 games. How many different series of games is possible? (i.e., Team A wins the series by winning games 1, 2, 4, and 6)

Would it just be 7 choose 4?
• Mar 13th 2011, 04:41 PM
Plato
Quote:

Originally Posted by jellyksong
In the World Series, two teams play each other until one team wins 4 games. How many different series of games is possible? (i.e., Team A wins the series by winning games 1, 2, 4, and 6)
Would it just be 7 choose 4?

This is perhaps the most famous question in probability.
It may well date back to the eleventh centenary.
Playing any series of seven games will determine a winner. RIGHT?
“Who has four wins, there are no ties’s”.
$\sum\limits_{k = 4}^7 {\binom{7}{k}2^{ - k} } = 0.5$ for each team.
• Mar 13th 2011, 04:49 PM
Random Variable
If Team A wins in 4 games, they must win the first three games. If Team A wins in 5 games, they must win 3 out of the first 4 games. If Team A wins in 6 games, they must win 3 out of first 5 games. And if team A wins in 7 games, they must win 3 out of the first 6 games.

So number of ways Team A wins is $\binom{3}{3} + \binom{4}{3} + \binom{5}{3} + \binom{6}{3}$

And the number of ways Team B can win is obviously the same.
• Mar 13th 2011, 06:10 PM
Plato
Quote:

Originally Posted by Random Variable
If Team A wins in 4 games, they must win the first three games. If Team A wins in 5 games, they must win 3 out of the first 4 games. If Team A wins in 6 games, they must win 3 out of first 5 games. And if team A wins in 7 games, they must win 3 out of the first 6 games.So number of ways Team A wins is $\binom{3}{3} + \binom{4}{3} + \binom{5}{3} + \binom{6}{3}$ And the number of ways Team B can win is obviously the same.

Do you understand that none of that makes any difference?
Team A wins if any of the sequences $AAAABBB$ occurs?
Suppose that we require that seven games be played period no matter the outcomes. Do you see that any string of four A's and three B's mans that team A wins?
As I said above, this question has a long history.
I can trace it back ot at least the $11^{th}$ century.
• Mar 13th 2011, 07:02 PM
Random Variable
Well, the answer you posted makes no sense. Team A wins in 35/16 ways?

EDIT: Did you mean $\binom{7}{4}$ ways?