p = probability of success = .997 (897 / 900)
 q = probability of failure = .003 (1.0 - .997)
 n = number of trials       = 2323
 X = number of successes    = 2323

Applying these to the binomial probability formula, we get:

P(2323) = 2323! / ((2323 - 2323)! * 2323!) * .997**2323 * .003** (2323-2323)
         = .0009307922

So we conclude that the probability that our trials with this patch
applied achieved exactly 2323 successes because of chance alone is . 0009.

Not prematurely rounding p to a useless precision gives you

        p**2323 ~ 0.000428

even.  And that just calculates the chance that 2323 tries all
succeed given that the chance for one to succeed is 897/900; it
doesn't compare two hypotheses at all.


Segher


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