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  • probability theory - Monkey typing ABRACADABRA and gamblers . . .
    Problem: A monkey is sitting at a typewriter, typing a letter (A-Z) independently and with uniform distribution each minute What is the expected amount of time that passes before ABRACADABRA is sp
  • Infinite monkey theorem and numbers - Mathematics Stack Exchange
    I had a discussion with a friend about the monkey infinite theorem, the theorem says that a monkey typing randomly on a keyboard will almost surely produce any given books (here let's say the bible) I believe this experience can be reduced to choosing a random sequence among real numbers:, strictly speaking the monkey could type a sequence looking like 1 3
  • Creating explicit martingale descriptions for the Monkey typing ABRACADABRA
    A Problem Related to Monkey Typing 13 Monkey typing ABRACADABRA and gamblers 0 Stopping times and
  • Conditional probability for a monkey to randomly write a sentence
    We all know the statement that a monkey, typing random keys, given enough time, will type anything we want Say what I want is the sentence: "This is cool" There are 12 characters, if the monkey's keyboard has 30 keys (the actual number is irrelevant), there will be $\frac{1}{30^{12}}$ probability to write that sentence
  • probability - Expected time to type a certain sequence - Mathematics . . .
    $\begingroup$ The plus one is to account for the current step For the first equation, if the first step is an A, then the expected number of steps is 1 (the step that gave an A) plus the expected number of steps after an A Likewise, if the first step is a B or C, then the expected number of steps is 1 (the step that gave a B or a C) plus the expected number of steps generally, E, since a B
  • probability - Question regarding monkeys and probabilities . . .
    So the question as presented is given $10^{10}$ monkeys randomly typing away on a typewriter with 44 keys (no capitals, just 26 letters and 18 special characters) at a rate of $10$ keys per second for $10^{18}$ seconds, what is the probability that a specific sequence of $10^5$ characters was typed by any one of the monkeys
  • An easy-to-understand interpretation of Infinite monkey theorem
    If we have $100$ billion monkey-blocks, either from $1$ monkey typing $600$ billion characters or $100$ billion monkeys typing $6$ characters each the chance that there is no recognized 'banana' is $0 0017$
  • Are there any practical implications of Infinite Monkey Theorem?
    But the odds of typing Hamlet on a typewriter randomly are less than 1 out of 26^130,000 since Hamlet has about that many characters We'll round that down to 10^130,000 for simplicity If you loosen the conditions to allow any of a million different written works over 130,000 characters to be generated randomly you knock about 6 zeros off of that 130,000
  • Infinite monkey theorem independent of number of monkeys
    If you have assigned each portion of the text to some particular monkey in advance, it is the same as having a single monkey that occasionally takes a break between typing sprees It gets more interesting when you can choose the order in which to put the typed strings, etc and only then more monkeys can have better chance of typing your favorite text $\endgroup$
  • Proof of infinite monkey theorem. - Mathematics Stack Exchange
    $\begingroup$ @Aditya: If you prefer, more intuitively, you can complete the demonstration as follows: One monkey fails to type the CWOS (from the beginning) with probability $1-1 m^N$ Two monkeys fail to type it with probability $(1-1 m^N)^2$





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