p(5 sets of twins in the SD state football tournament)

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Amit Kumar
Amit Kumar 2011-11-11
All,
I'm guessing that I'm vastly over- or under-thinking this one, but here it is.
Question: In the South Dakota State High School Football Tournament, there are 12 teams competing with a total across all 12 teams of 555 players. Among the 555 players there are 5 sets of twins (i.e., 10 people who have a twin also playing in the tournament). What is the probability of that occurring?
Given that the p(being a twin) is around .032, then one would expect to see ~13 twins in a random sample of 555 people. So, seeing 10 twins is not all that improbable. In fact, p(seeing only 10 twins) is lower than .032, which is what one would expect, though not all that anomolous.
I may be complicating things by asking something like: OK, so if 5 of the players are a twin, what is the p(their OTHER twin also appears in the tournament). This seems like a much more complicated question that begs for a lot of information I don't have. It seems that twins would be raised in similar settings/environments and whether identical or not, would have a lot of exposure to the same opportunities, likes, dislikes, etc. So seeing Both on the same team, would not be all that improbable.
Am I missing something? Missing a lot?
Any help would be most welcome.
Thanks,

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Daniel Shub
Daniel Shub 2011-11-11
Don't confuse expectation and probability. The expectation is that if you flip a fair coin two million times that you will get heads 1 million times, but the probability of getting exactly 1 million heads in 2 million flips is really small (0.00056).

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