Infinite monkey theorem

The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. More precisely, under the assumption of independence and randomness of each keystroke, the monkey would almost surely type every possible finite text an infinite number of times. In this context almost surely means that the event has probability 1, and the monkey is a metaphor for an abstract device that produces an endless random sequence of letters and symbols. The theorem can be generalized to any infinite sequence of independent events whose probabilities are uniformly bounded below by a positive number. One of the earliest uses of the monkey metaphor is by the French mathematician Émile Borel in 1913, and Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics. For physically meaningful numbers of monkeys and lengths of time the result is reversed, because the probability of reproducing even one page of Shakespeare is unfathomably small.