It has been said that enough monkeys, pounding on enough keyboards for enough time, will eventually...

It has been said that enough monkeys, pounding on enough keyboards for enough time, will eventually produce the complete works of William Shakespeare. Let’s examine this.

Suppose we have 10 billion galaxies, each containing 10 billion planets populated by 10 billion immortal monkeys with extreme insomnia. We provide each with a keyboard consisting of 26 keys (we won’t insist on capitalization, punctuation, or even spaces). The monkeys proceed to randomly strike 10 keys per second for the age of the universe (10^18 s).

To improve our odds, we’ll calculate the probability that one of our 1030 monkeys produces a text sequence that merely matches Hamlet: ~1.33 x 105 alphabetic characters.

(a) Show that the probability of any given sequence of 1.33 x 10^5 characters typed at random to match the characters of Hamlet is approximately (1/26)^133300 = 10^-188191

(b) Show that the probability of at least one monkey producing a copy of Hamlet in the age of the universe is approximately 10^-188142

Solutions

Expert Solution

genius_generous answered 1 year ago

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