Somewhere in pi (at some insane offset) is the entire work of William Shakespeare.
Is that the basic idea here?
You have to calculate the probability of a monkey coming up with a work of Shakespeare, and then subtract that from 1 to get the probability of a monkey coming up with anything other than a work of Shakespeare, and then figure out what power N to raise that to (N attempts) for it to cross below some confidence value, like 0.05 ... then subtract that from 1 in order to get the probability of a monkey coming up with a work of Shakespeare after that many attempts.
(no matter how high N is, you will never get 0, so no matter how many times you attempt, you always "could" still not produce a work of Shakespeare, because there's always a chance that none of those attempts worked)
Then calculate how much time that might take (actually, you might even have to account for failed attempts that are shorter or longer than a work of Shakespeare, so you might even have to start with time rather than number of attempts, but I digress) and you have a possible figure for "how much time it would take to have a certain probability of a monkey having come up with a work of shakespeare" and oh dear I may have missed the joke