The Infinite Monkey Theorem states that a monkey pressing keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a particular finite text, such as the Bible…
Consider a single biblical phrase, “In the beginning, God created the heavens and the earth.” How long would it take a monkey to type this phrase?
Assume there are 93 symbols on a keyboard, the phrase contains 56 letters (including spaces and the period).
If the probability of hitting the correct key on the typewriter is l/n, where n is the number of possible keys, then the probability of the monkey correctly typing 56 consecutive characters in the target phrase is, on average, (1/93)^56, which means that the monkey would have to try more than 10^100 times, on average, before getting it right.
Mathematical analysis reveals that the monkey, after only 407 trials, would have a 50/50 chance that the correct sentence was typed.
If the monkey (or any abstract device that produces a random sequence of letters ad infinitum), pressed one key per second, it would be typing for well over the current age of the universe, however, mathematically, it is possible the monkey would eventually achieve it.1
- http://mathematica.tumblr.com/post/40035417792/the-infinite-monkey-theorem-states-that-a-monkey [↩]