The Infinite Monkey Theorem is a popular saying that suggests that a monkey hitting keys at random on a keyboard for an infinite amount of time will eventually type out a given text, such as the complete works of William Shakespeare.

The theorem is often used to illustrate the concept of probability, as well as the fact that even very unlikely events can occur given enough time.

#### How do you prove the infinite monkey theorem?

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type out a given text, such as the complete works of William Shakespeare.

The proof of the theorem relies on the fact that the probability of the monkey typing out any particular sequence of letters is 1/n, where n is the number of possible sequences of letters. Thus, the probability of the monkey typing out the complete works of Shakespeare is 1/n, where n is the number of possible sequences of letters in the complete works of Shakespeare.

The number of possible sequences of letters in the complete works of Shakespeare is n = 26^(5.5 million), which is a number so large that it is effectively infinite. Therefore, the probability of the monkey typing out the complete works of Shakespeare is 1/n, which is effectively zero.

Thus, we can conclude that the monkey will almost surely type out the complete works of Shakespeare if it hits keys at random on a keyboard for an infinite amount of time.

##### Who made the infinite monkey theorem?

The infinite monkey theorem is a thought experiment that was first proposed by French mathematician Ă‰mile Borel in 1913. The theorem states that if a monkey were to type randomly on a keyboard for an infinite amount of time, eventually they would produce any given text, such as the complete works of William Shakespeare.

The theorem is often used to illustrate the idea that all information, regardless of how complex or seemingly random, can be reduced to a simple set of underlying rules or patterns. How long would it take a monkey to type Hamlet? There is no definitive answer to this question, as it would depend on a number of factors, including the monkey's typing speed, accuracy, and understanding of the play. However, a rough estimate could be made by assuming that the monkey would type at a rate of approximately 10 characters per second, and that the play consists of approximately 4,000 characters. This would mean that it would take the monkey approximately 400 seconds, or 6 minutes and 40 seconds, to type the entire play.

#### How do you use the infinite monkey theorem?

The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type out a given text, such as the complete works of William Shakespeare.

The theorem has been used to justify the notion that all works of literature, music, and art could be eventually produced by random chance, given enough time.

In practice, the theorem is often used as a thought experiment or a humorous way to illustrate the fact that very large sets of data can contain anything that you might want to find, given enough time and effort.

For example, if you have a very large set of text data, you could search through it for any particular string of characters, no matter how long or how unlikely it is, and you would eventually find it given enough time. How fast can a monkey type? A monkey can type at a rate of about 10-20 words per minute.