Suppose you have a set of digits, for the sake of simplicity we'll make them binary, how would you determine the probability that the set is random? For example, given the following 3 strings of numbers...(adsbygoogle = window.adsbygoogle || []).push({});

1111111111111111111111111111111111111111111111111111111111111111

0010010000111111011010101000100010000101101000110000100011010011

1101011111001000000000011101111011111010010101011111101010110110

The first appears non random while the second and third appear random. In reality, only the third actually is random. Given a truly random string of 1s and 0s all 3 are equally likely. So If I didn't know the origin of the numbers how would I compute a probability that they were generated randomly?

For the sake of simplicity assume that if they are random then the probability of 1 is the same as the probability of 0 and that each digit selected without consideration of any other digit.

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# How to compute the probability that a given set of numbers is random

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