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# Probability question about the UEFA Champions League Watch

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1. I don't know but I can give you the probability of Tottenham going through to the quarterfinals. 5/100
2. Assuming all draws within the rules are equally likely (which I don't think is that unreasonable, but probably should be checked)

Then I get the following result:

There are 6304 valid draws of which
1395 are Bayern Munich, 1395 are Schalke, 1757 are Real Madrid, 1757 are Barcelona

Giving probabilities of 0.221 for German teams and 0.279 for Spanish.

(Of course, this all relies on me understanding the rules properly and being able to code, none of which should be taken for granted at the moment)

Since this agree with sonofdots' simulation, I'm pretty happy with them.
3. (Original post by SimonM)
Assuming all draws within the rules are equally likely (which I don't think is that unreasonable, but probably should be checked)

Then I get the following result:

There are 6304 valid draws of which
1395 are Bayern Munich, 1395 are Schalke, 1757 are Real Madrid, 1757 are Barcelona

Giving probabilities of 0.221 for German teams and 0.279 for Spanish.

(Of course, this all relies on me understanding the rules properly and being able to code, none of which should be taken for granted at the moment)

Since this agree with sonofdots' simulation, I'm pretty happy with them.
Brilliant, cheers.

My initial thought was considering what all of the possible match ups were, but obviously they could be in different orders etc. and restrictions 2) and 3) would mean that some match ups would be more common than others.

But if it's considering all the possible draws, then I think each draw would be equally likely, and so that would be spot on.

Thanks a lot!
4. Hmm, interesting - the effect was significantly greater than I had approximated.

Still wonder what would've happened if all the teams we were allowed to draw had already been chosen...
5. (Original post by n1r4v)
Brilliant, cheers.

My initial thought was considering what all of the possible match ups were, but obviously they could be in different orders etc. and restrictions 2) and 3) would mean that some match ups would be more common than others.

But if it's considering all the possible draws, then I think each draw would be equally likely, and so that would be spot on.

Thanks a lot!
From all possible (valid and invalid) draws, there is no possibility of a German clash, so Arsenal drawing Schalke or Bayern Munich does not "free up" potential clashes between Italian/Spanish teams, whereas Arsenal drawing Real Madrid or Barcelona removes some of these clashes, yielding more valid draws.

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Updated: December 17, 2010
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