1/9/2024 0 Comments England library monkeyThe probability that infinitely many of the E k occur is 1. Because each block is typed independently, the chance X n of not typing banana in any of the first n blocks of 6 letters is Less than one in 15 billion, but not zero.įrom the above, the chance of not typing banana in a given block of 6 letters is 1 − (1/50) 6. Therefore, the probability of the first six letters spelling banana is 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. Suppose that the keys are pressed randomly and independently, meaning that each key has an equal chance of being pressed regardless of what keys had been pressed previously. 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.Ĭonsider the probability of typing the word banana on a typewriter with 50 keys. As an introduction, recall that if two events are statistically independent, then the probability of both happening equals the product of the probabilities of each one happening independently. ![]() There is a straightforward proof of this theorem.
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