A repeated digit in the PIN

A 4-digit PIN is chosen with each digit uniform and independent in {0,,9}\{0,\dots,9\}. What is the probability that at least one digit is repeated (some digit appears more than once)? (to 3 decimals)

Show hints (2)+
  1. 'At least one repeat' = 1 − P(all four distinct).
  2. All-distinct count is 10·9·8·7 over 10⁴.

Answer

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0.496

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Asked at: EV & Betting Games, Mixed Quant & Coding

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