Concevons qu’on ait dressé un million de singes à frapper au hasard sur les touches d’une machine à écrire...

Emile Borel

edit: added the attribution for the quote

Ignoring punctuation, spacing, and capitalization, a monkey typing letters uniformly at random has a chance of one in 26 of correctly typing the first letter of Hamlet. It has a chance of one in 676 (26 × 26) of typing the first two letters. Because the probability shrinks exponentially, at 20 letters it already has only a chance of one in 2620 = 19,928,148,895,209,409,152,340,197,376[d] (almost 2 × 1028). In the case of the entire text of Hamlet, the probabilities are so vanishingly small as to be inconceivable. The text of Hamlet contains approximately 130,000 letters.[e] Thus, there is a probability of one in 3.4 × 10183,946 to get the text right at the first trial. The average number of letters that needs to be typed until the text appears is also 3.4 × 10183,946,[f] or including punctuation, 4.4 × 10360,783.[g]

Even if every proton in the observable universe (which is estimated at roughly 10^80) were a monkey with a typewriter, typing from the Big Bang until the end of the universe (when protons might no longer exist), they would still need a far greater amount of time – more than three hundred and sixty thousand orders of magnitude longer – to have even a 1 in 10^500 chance of success. To put it another way, for a one in a trillion chance of success, there would need to be 10360,641 observable universes made of protonic monkeys.