The meaning of “never” and the power of a good editor. It has been said that “si

Question

The meaning of “never” and the power of a good editor. It has been said that “six monkeys, set to strum unintelligently on typewriters for millions of years, would be bound in time to write all the books in the British Museum.” This statement is nonsense, for it gives a misleading conclusion about very, very large numbers. Could all the monkeys in the world have typed out a single specied book in the age of the universe? Suppose 1010 monkeys have been seated at typewriters throughout the age of the universe, 1018 s. This number of monkeys is about two times greater than the present human population of the earth. We suppose that a monkey can hit 10 keys per second. A typewriter may have 44 keys; we accept lowercase letters in place of capital letters. Assuming the Shakespeare’s Hamlet has 105 characters.

(a) What is the probability that a monkey-Hamlet will be typed in the age of the universe?

(b) Ontheotherhand,suppose6monkeyshadasupermonkey-editor whokeptallcharactersmatching Hamlet (in character and location). After the rst 100,000 characters, the monkey-editor continues to keep the matching characters in place, and overwrites the incorrect characters with the subsequent random keystrokes from the 6 monkeys. How long does it take for these 6 monkeys to produce a Hamlet?

Explanation / Answer

There are 44 keys on a typewriter, so the probability that the first letter is correct is 1/44. The probability that the second letter is correct is 1/44, etc. Since we need all the letters to be correct, we need to raise 1/44 to the power of the number of letters in Hamlet: 1/ 44^100000 = 44^100000 = 10log10(44)×100000 = 10164345

where I have used the fact that log10(4) = 1.64345.

b)

Since a monkey types 10 letters a second, and the age of the Universe is 1018 seconds, the total number of letters that can be typed by one monkey in that time is 1019. The monkey is able to start with any of them except for the last 1019 (105 1) 1019 of them. Now, the probability that a sequence of 105 letters will yield Hamlet is given in equation 19. Since there are 1019 characters that it can start typing with in order to create Hamlet, the probability that one monkey will type Hamlet in the age of the Universe is

P(Hamlet, 1Monkey) = 101910164345

so the probability that 1010 monkeys will do it is (just multiplying by 1010):

P(Hamlet) = 1010101910164345 = 1016431

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