Probability of two similar pins?
Hello, my wife and I asked ourselves the following question today.
She is with Volksbank and has her PIN (e.g. 3677)
Now we have opened a joint account at the Sparkasse and she has received the PIN (3688) for her card.
What is the probability that this PIN combination will be issued by two different institutions?
The pin numbers are of course not the real ones but in our case the first two digits are the same and the last two are 11 higher.
There are several years between the accounts being opened. Perhaps this is relevant for the calculation.
The probability of a 4-digit PIN is 10 to the power of 4, but an identical PIN for two accounts in the same name exceeds our mathematical capabilities 🥲😅
We would be pleased to receive an answer.
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The probability for two identical PINs is 1:10.000 (probably even slightly higher because I assume that not all numbers are awarded from 0000 to 9999).
The probability for two PINs with two identical digits at the first two digits is 1:100.
Now it is necessary to define what is called “similar” in order to continue to reckon – but as unlikely as the spontaneous materialization of a petunie and a pottery is not.
You have the pin abcd, then there are 100 other pins that also start off.
In total there are 10000 pins (if all are awarded), the probability of getting one of these 100 is therefore 100/10000 = 1%.
That’s not so small. Imagine you have 100 married couples who each apply for a PIN for each of the two partners. Then one would expect the two first digits to match one pair.
Of course it is possible.
The numeric komi aren’t infinitely possible – just at 4 numbers.
That is possible, of course, we have exactly this case.
We just wanted to have a probability calculation on this 🤔
That it seems quite likely that at 10,000 possibilities two people get the same PIN is uncertain at first sight.
In fact, however, the matching bank card also needs. And if I remember correctly, the card is locked and/or pulled in by the machine after three failures.
There are theoretically 10,000 possibilities – at least if 0000 and all other combinations are also awarded. No matter which number one PIN has, the probability that the other is the same is 1:10.000. If you think that in a small town with 50,000 inhabitants there may be 50,000 cards (because some have one or more), then 5 of people will have the same PIN as you.
there are at four places maximum 10000 possible combinations, at 85 million Germans, of which certainly have more than half an account, some even more, each individual pin appears several thousand times.
You can not calculate the probability because the numbers are not completely random, but are freely selectable in many cases.
(1:9999)2
No. The first pin you can choose freely, only when selecting the second PIN it becomes interesting.
It’s like having two equal pins. Except 0000 also applies. Then it is 1:100000000
No. What you calculate is the probability that both have a specific PIN. So: The probability that both have the PIN 3456 is
Person A has the PIN 3456 = 1/10000
Person B has the PIN 3456 = 1/10000, so total: p = 1/100000000
But the probability that both have the same PIN is
Person A has some PIN = 1
Person B has exactly this PIN = 1/10000.
You can also explain it like this: I look at the couples (PINA, PINB).
There are 10000 variants for PINA and 10000 variants for PINB, i.e. a total of 100000000.
There is exactly one pair in which both have the PIN 3456, namely (3456, 3456), therefore the probability is 1/100000000.
But there are 10000 couples in which both have the same PIN, namely
(0000, 0000)
(0001, 0001)
(0002, 0002)
…
(9999, 9999).
The probability that both have the same PIN, therefore 10000/100000 = 1/10000.
Of course, four-digit PNs are not exclusive. You also only work GEMEINSAM with the map.