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2,000,000 Coin Tosses (Posted on 2003-03-03) Difficulty: 2 of 5
If a coin is tossed 2,000,000 times, what is the probability that it will come up exactly 1,000,000 times each heads and tails?

See The Solution Submitted by Charlie    
Rating: 3.0000 (8 votes)

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re: Basic idea | Comment 6 of 10 |
(In reply to Basic idea by Alan)

The catch here Alan is that the outcome is NOT dependant on order. You've correctly begun the process by showing there to be 2^2000000 possible "ordered" outcomes, but now you have to find some way of grouping them so that you include all the possible ways of flipping the desired number of heads. For example, on a much smaller scale, with two flips you could get;
HH
HT or TH
TT
So the prob. here is 2/4, not 1/4. I hope this gets my point across.

  Posted by Cory Taylor on 2003-03-08 07:15:31

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