10:56 PM — More Monkeys RE: Infinite Monkeys throw Infinite Shit at Infinite Computers

Tortoise points out to me that "the probability of one monkey typing Hamlet is not 0, it is roughly 1/50^200,000, where 50 is the number of allowed characters and 200,000 is the number of characters in Hamlet." The probability that any single monkey types all A's is the same. The infinite monkeys could theoretically ALL type all A's. Or all B's, or any other combination that isn't Hamlet. It's possible. However, the probability of it is zero.

We will ignore any characters before or after the script of Hamlet. Let x=50^200,000, that is, the number of possible documents the length of Hamlet. In 200,000 characters, there are x possible documents. Looking at one specific monkey's output, the chance of that particular document being Hamlet itself is 1/x.

• The chance of that single document being anything BUT Hamlet is y=1-(1/x)=(x-1)/x<1.


• The chance of TWO documents being non-Hamlet is y^2=1-2/x+(1/x)^2~1-2/x.


• The chance of 3 documents being non-Hamlet is y^3=1-3/x+...


• The chance of infinity-many documents being non-Hamlet is y^infinity=1-infinity/x+... =0.


• Q.E.D.

My brain hurts.

For more laughs, check out the Brunching Shuttlecocks'
article on other things the monkeys might type.   ¶ permalink | 0 musings