Good points plaw. As I thought about it, your points below are what you've said before, but just put in another way. Let me explain...
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Originally posted by plawrence: At first, I thought I was incorrect, and the odds were 4096 x 4096. But then I figured, if there are 4096 ways to arrange the team, and CC arranged it one way, whoever else had a 1/4096 chance of arranging it the same way.
This was exactly your point before... Given Bethie's team (which we can set in stone), SP has a 1 out of 4096 chance of matching it. The key is that we already know what Bethie picked a team.
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Originally posted by plawrence: If CC chooses heads first, then the chances of SP choosing heads is 1/2. But not knowing if Beth took heads or tails, i.e. if they "flip" simultaneously, then SP still has a 1/2 chance of [b]matching (H-H or T-T), or not matching (T-H, H-T).[/b]
This too is also the same point. We know that Bethie picked one of the 4 power forwards. Knowing that she picked one, someone else has a 1 in 4 chance of picking the same one. However, there's a slight difference in asking about the probability that Tim Duncan is picked. Bethie has a 1 in 4 chance. So does another person. Together, they have a 1 in 16 chance of both picking Tim Duncan.
As for your above example, you're right that there is a 1 in 2 chance that they match. There is also 1 in 4 chance that they both have heads.
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Originally posted by plawrence: I know there's a scenario where 4096 x 4096 is the correct answer, I just don't know what it is.
Maybe here's a way to clarify the question:
What are the odds of two players picking the same point guard, the same shooting guard,..., and the same coach? 1 in 4096
What are the odds of two players both picking Tyronne Lue, T-Mac,..., and Frank Johnson? 1 in 16,777,216.
What do you think? I think this is a problem, not of statistics, but of semantics.
