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Infinite Monkey Theorem

Posted by Diego Fonstad
Diego Fonstad
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on Wednesday, 30 March 2011
in Great Explanations

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.

References: http://en.wikipedia.org/wiki/Infinite_monkey_theorem
http://www.junkworthknowing.com/technology/the_infinite_monkey_theorem

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Tags: Math
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