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?
(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.
re: Basic idea
