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Would it ever actually get to 1?
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Well, if you repeat the test X number of times, it will never be 1, but, yes, it is kinda to do with limits, the more times you do it, the closer the probability gets to 1, but it never quite reaches 1. Thus, it's limit, is 1.
But of course, if you do it an infinite number of times, then let's say we do it 5000 times and that still fails, we can always try doing a 5001 time and there is a chance we will succeed, so we keep doing it, eventually, we have got to succeed because there is always this chance of succeeding next time... Ahaha, kinda like gambling I suppose
But hmm... I suppose you could try and argue that even if you went on and on forever you would never get that random combination you are looking for simply because your "random number generator" whatever that maybe, in this case a chimp, doesn't ever pick it, even though there is the possibility of it choosing it... Hmm... That is actually an interesting point I hadn't considered initially, and I'm not sure that the previous argument covers it

But then, if the chimp never types the shakespeare play, is the probability of the chimp typing a shakespeare play on any given attempt really greater than 0? Hmmmmmmmmmmmmm... Have to think about that one
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Now prove how often the chimp must repeat this to succeed with 98% possibilty
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well let p = probability of chimp succeeding on first attempt
Then assuming Shakespeare's works are 6 million chars then p = 1/(60^6,000,000) = a very very very very very very very small number (assuming there are 60 chars on a keyboard... Which is probably wrong)
Then we bung this value of p into the binomial distribution testing it with different values of n (number of trials) e.g. 1,2,3,4,5,6... and so on. Until we get p > 0.98 at which point n is the required number of trials to get a probability of 98% of succeeding
Now the really interesting part here is how the fuck you would handle all that computation, by hand it would take forever and most computers will fuck up because the number is so small... Plus it might also take forever on a computer anyway... But at least the algorithm is there
Now who thought chimps could make life so complicated?
