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Advanced Math/re; odds and probabilities


I have a question regarding bank card pin numbers. what is the probability and odds of two friends (known him for 17 years) have the same pin number for a debit card. these pin numbers were assigned by two different banks and neither pin number was changed by either myself or my friend.

interested to know what the odds are.


There are 10,000 possible four-digit PINs (0000 through 9999). I am assuming that your PIN is four digits, that is the most common. Your relationship as friends etc. is not relevant, and we can assume the banks assign PIN randomly, so the probability is 1 in 10,000 that your PIN numbers match.

Now, in reality, the probability is slightly higher, because banks avoid a few very bad PINs (like 0000, 1111, 2222, 1234, etc.), putting the odds somewhere between 1 in 9,990 and 1 in 9,950 or thereabouts. That is still very close to 1 in 10,000.

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.


I am a PhD educated mathematician working in research at a major university.


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BA mathematics & physics, PhD mathematics from a top 20 US school.

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