### Brain Teasers

# World Series

Fun: (2.25)
Difficulty: (2.72)
Puzzle ID: #8787

Submitted By: lesternoronha1 Corrected By: shenqiang

Submitted By: lesternoronha1 Corrected By: shenqiang

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.Probability

The world series consists of up to seven games, the first team to win four wins the series. Team A will play in their home field for games 1, 2, and 6 and 7 if necessary. Games 3, 4, and 5 (if necessary) will be played at team B's home field. Assuming each team has a 50% chance of winning every game, which team is more likely to have the home field advantage the majority of the time? For extra credit what is the expected number of games played in each home field?

### Answer

In general the probability of either team winning exactly 3 out of n (n>3) games is (n-1)*(n-2)*(n-3)/(3*2^n).For a series to last exactly n games at least one team must have won exactly 3 out of the last (n-1). Thus:

The probability of the series lasting 4 games is 1/8.

The probability of the series lasting 5 games is 1/4.

The probability of the series lasting 6 games is 5/16.

The probability of the series lasting 7 games is 5/16.

The expected number of games played in team A's home field is: 2*(1/8) + 2*(1/4) + 3*(5/16) + 4*(5/16) = 188/64.

The expected number of games played in team B's home field is: 2*(1/8) + 3*(1/4) + 3*(5/16) + 3*(5/16) = 184/64.

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## Comments

wutever.

Here's a thought: if the teams have a 50% chance of winning any game, then how could there be a home field "advantage"?

you said that both teams will play at their home feild for game 5. That would be a little difficult.

Well, if one of the teams happens to be the Cubs...

Good point Giz! But he didn't say it was a competitive advantage. Maybe the advantage is you don't have to travel so far or the local press will publish your photo on the front page. Maybe that cute freshman your are keen on might come to watch!

Fantastic puzzle!

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