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?

I don't know what the numerical solution is because we're dealing with relatively large numbers. But here's the symbolic one.

The total number of outcomes is 2^(2000000). The total number of expected outcomes is 2000000 choose 1000000, which is 2000000!/((1000000!)*(2000000-1000000)!). So the probability is just the ratio of the two of them.

If I remember correctly, you should be able to model this with a binomial distribution and then get an estimate with a normal distribution approximation. The mean is N*p (1000000 in this case) and the standard deviation is sqrt(N*p*(1-p)) which is 500*sqrt(2). Then you can use the Z-Charts, with the continuity corrections of 1/2, to determine the approximate value.

I don't have a z-chart so I can't get a numerical solution. For those of you who know what I'm talking about and have a z-chart, please post the answer.

Posted by np_rt on 2003-03-03 07:57:51