A popular Dilbert cartoon strip (popular among statisticians, anyway) shows an a

Question

A popular Dilbert cartoon strip (popular among statisticians, anyway) shows an allegedly “random” number generator produce the sequence 999999 with the accompanying comment, “That’s the problem with randomness: you can never be sure.” Most people would agree that 999999 seems less “random” than, say, 703928, but in what sense is that true? Imagine we randomly generate a six-digit number, i.e., we make six draws with replacement from the digits 0 through 9.

1. Here’s a real challenge: what is the probability of generating a sequence with exactly one repeated digit?

Explanation / Answer

probability of generating a sequence with exactly one repeated digit

The digits can be from 0 to 9

The sequesnce can be 000000, 111111,222222,......999999 (10 sequences)

The prob = 10*(1/10)^6 = 0.1^5 = 0.000001

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