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Infinite Monkey Theorem
Teachable Moment: This wonderful thought experiment is a great way of exploring probabilities as they apply to multiple random events. The mere fact that it has infused its way into popular culture is a testament to its ability to engage thinkers.
The infinite monkey theorem, originally posited by Emile Borel, states that a monkey pressing keys at random on a keyboard for an infinite amount of time would eventually type a finite text.
The probability of typing that text is straight forward:
n= number of possible keys on keyboard
l = length of phrase being typed
probability = (1/n)^l
However, as the length of the phrase gets longer, the probability of the monkey NOT typing the text approaches infinity P=1-(1/n)^l... but there's always a tiny probability that the phrase is typed... that's the problem with infinity!
The probability goes down significantly if we can save characters that are typed correctly as we go along.