2003-10-20 03:19:59 ET|
I was just sitting at my computer when my friend Joe sent me the following question.
Suppose that 10^10 monkeys have been seated at typewriters throughout the age of the universe 10^18s. We suppose that a monkey can hit 10 keys/second. A typewriter may have 44 keys. Assuming Hamlet has 10^5 characters, what is the probability that the monkeys will come upon the correct sequence of hamlet?
Here is what I came up with.
There are 10^18 seconds given, So that is 10^19 keys/monkey after all the time.
Now the play can start anywhere before the last 10^5 keys and still be complete, so that gives us
10^19 - (10^5 -1) = 9999999999999899999 ~ 10^19.
(Note: The approximation of 9999999999999899999 ~ 10^19 gives an error of less than 10^-10, which I find to be acceptable.)
Times the number of monkeys (10^10) gives us 10^29 different papers total.
The number of possible different papers is 44^(10^5).
So the probability that one paper is correct is (10^29)/(44^(10^5))
Which is approximately 5.399*10^-164317
(Monkeys will not write Hamlet. I know I'm sad too. -Bill.)
(Note: This is assuming that the monkeys don't plagiarize off each other. and that the monkeys don't stop typing and start throwing poo at each other.)
P.S. This is probably (hehe probability) the only time my Subject will not be either a number or the sum of two primes.