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Probability & Statistics/Binomial distribution question

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Question
Hello Clyde,

I was taking a look at a question on this link:

http://stattrek.com/probability-distributions/binomial.aspx?tutorial=stat

One of the question was about a team winning 4 games, 5 games, 6 games, 7 games.

Now, the team winning 4 games was clear given they both have a 50/50 chance of winning. It is however, the team winning 5 games that got me lost. This statement :

"Now let's tackle the question of finding probability that the world series ends in 5 games. The trick in finding this solution is to recognize that the series can only end in 5 games, if one team has won 3 out of the first 4 games. So let's first find the probability that the American League team wins exactly 3 of the first 4 games."  

is what I don't understand. Why must a team win 3 games out of first 4 games for the game to end? Please, help me understand why.

Thanks

Answer
If the team wins four games out of five, you seem to think there are these possibilities:

L W W W W

W L W W W

W W L W W

W W W L W

W W W W L



And that might be right -- except that the last scenario isn't possible. You don't play the 5th game if the first four are wins.

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Clyde Oliver

Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

Experience

I am a PhD educated mathematician working in research at a major university.

Organizations
AMS

Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.

Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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