Question

Events of low probability can eventually happen if you observe enough trials. Find the probability that the first keystrokes a monkey types on a typewriter spell . Assume the typewriter has keys and that the monkey types randomly.

The probability is__

Answer 1

The probability of a monkey randomly typing a given sequence of four characters correctly on a typewriter with 50 keys is the product of the probabilities for each character, resulting in 1/6,250,000.

Step-by-step explanation:

The student asks about the probability that a monkey typing on a typewriter with 50 keys will type a specific sequence of characters. The probability of the monkey typing a specific character correctly is 1/50 since there are 50 equally likely choices for each keystroke. To find the probability of typing a particular sequence, we multiply the probabilities of each keystroke, assuming the keystrokes are independent.

Let's say the sequence is 'word'. The probability of typing 'w' first is 1/50, the probability of 'o' after that is 1/50, and so on for 'r' and 'd'. So, the probability of typing 'word' correctly in sequence is (1/50) * (1/50) * (1/50) * (1/50) = 1/6,250,000.

This example illustrates the law of large numbers, suggesting that over a large number of trials, the relative frequency of an event will approach its theoretical probability.