What apparatus do monkeys use in the "infinite monkey theorem" thought experiment?
The Infinite Monkey Theorem is a proposition that an unlimited number of monkeys, given typewriters and sufficient time, will eventually produce a particular text, such as Hamlet or even the complete works of Shakespeare.
There is a straightforward proof of this theorem. As an introduction, imagine, if two events are statistically independent, then the probability of both happening equals the product of the probabilities of each one happening independently. For example, if the chance of rain in Moscow on a particular day in the future is 0.4 and the chance of an earthquake in San Francisco on any particular day is 0.00003, then the chance of both happening on the same day is 0.4 × 0.00003 = 0.000012, assuming that they are indeed independent.
Suppose the typewriter has 50 keys, and the word to be typed is banana. If the keys are pressed randomly and independently, it means that each key has an equal chance of being pressed. Then, the chance that the first letter typed is 'b' is 1/50, and the chance that the second letter typed is 'a' is also 1/50, and so on. Therefore, the chance of the first six letters spelling banana is
(1/50) × (1/50) × (1/50) × (1/50) × (1/50) × (1/50) = (1/50)6 = 1/15 625 000 000,
less than one in 15 billion, but not zero.
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