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people are getting too wrapped up in monkeys are neglecting the issue.
i think this is a starting point:
an uncountable number of trials with a nonzero probability of a success results in an uncountable number of successes and an uncountable number of failures.
I am pretty certain that statement is true. they don't really talk about an infinite numbers of trials in probability class so I guess i am not 100%, instead they focus on useful things like the law large numbers. which actually might do more for this post.
http://en.wikipedia.org/wiki/Law_of_large_numbers
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I don't think any of us are getting too wrapped up in monkeys. Such a thing might not even be possible.