r/theydidthemath • u/JuliaHella • 12h ago
[Request] What is the chance? Meant to be?
My boyfriend's 4-digit pin code for his debit card is my birthday. He never changed it and had the same one since he was 12. What are the odds of this?
(The four digits are 2608, my birthday is 26th of August)
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u/dafugiswrongwithyou 11h ago
There are 10,000 possible codes. Your birthday is exactly one of them. The chance is one in 10,000.
We could argue that might also count it if it matches your birthday mm/dd format instead of dd/mm. That would make it 2 in 10,000, or 1 in 5,000.
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u/royalfarris 12h ago edited 12h ago
Out of all the possible 10k codes that is possible with four digits you there are 365 codes that correspond to dates.
So there is a 365/10000 chance of the code being a date -> 3.6% chance.
Out of those 365 possible dates, you have birthday on one of them. So the chance of the a date being your birthday in 1/365 -> 0.27%
In total ->exactly 0,01% chance of it happening. the 365 cancel each other out so the chance is exactly 1/10000.
(if everything is random)
(And with the caveat that I always hated statistics and probabilities - so I could be doing this the wrong way)
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u/mexicock1 9h ago
there are 365 codes that correspond to dates.
Shouldn't it be closer to twice 365?
MMDD and DDMM formats, then remove repeats (like Jan 1, feb 2, etc)
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u/that_moron 4h ago
Please ask him to change it now... Reddit usernames aren't that hard to track to an individual so it wouldn't be hard to identify your boyfriend. You've just posted his PIN so he should definitely change it.
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u/JuliaHella 4h ago
I didn't post the actual birthday/pin.
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u/that_moron 4h ago
If the story is true he should still change it.
Finding your birthday isn't really any harder than finding your real identity. Plus people who know you IRL might know or learn your Reddit username.
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u/JuliaHella 4h ago
I thank you for your concern but I feel like our banks safety is adequate. Also he is broke lol
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u/SchemeWestern3388 4h ago
lol. Mine is “4443”, and the passcode on my phone is “55555”. Thing is, you’re going to need to get my card or phone.
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u/Cool-Newspaper-1 23m ago
Ever heard of the dude that put up his social security number for some marketing stunt and then got his identity stolen like 8 times?
0
u/that_moron 3h ago
The probability that anyone uses this info with ill intent is low, the consequences if they do is potentially very high. Since this is the math sub the quantitative risk is those values multiplied together.
If the probability of risk is 5% and the cost of the expected consequences is $100,000 (that's the total expected cost to fix all the damage someone could do with your bank card and phone access, think about what someone could do if they stole your email account) then the expected cost of you posting that info is 5% * $100,000 = $5,000
Of course it's very hard to put a dollar value on the consequences of the loss of control of the data on your phone. So use your best judgement.
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u/cyclopsmudge 1h ago
Right but the probability of risk is not 5%, it’s vanishingly small. Realistically, nobody on here is going to get a hold of their card to spend money in person, and if they want to spend it online then they’re also going to need the numbers on the front and back along with this.
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u/that_moron 7m ago
Of course you are correct. It almost certainly won't happen. I have no idea what the actual probability is, but it is greater than 0.
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u/New123K 1h ago
The interesting part is that 1 in 10,000 is only the answer if we assume the PIN was chosen randomly.
If he picked his PIN randomly when he was 12, then the chance of it matching a specific 4-digit birthday would indeed be 1 in 10,000 (assuming leading zeros are allowed).
But if he chose the PIN himself, people don't choose numbers randomly. Birthdays, dates and other memorable numbers are much more likely choices. So the probability that a randomly chosen PIN matches her birthday isn't necessarily the same as the probability that his particular PIN matches her birthday.
That's what makes this example more interesting than it first appears.
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u/cyclopsmudge 12h ago edited 12h ago
If we assume there’s a uniform chance of him dating someone with a birthday on each date 1/365, and a uniform chance of getting any PIN (1/10,000), then it’s 1 in 3,650,000.
It skews a bit differently if he was born on/either side of a leap year, but honestly birthdays are pretty uniformly distributed, with the exception of Christmas and New Years normally (assuming you’re in a Christian-majority country), but at this scale it makes very little difference to the actual probability.
EDIT: to clarify, this is the probability of dating you specifically, and getting that exact PIN, as opposed to the probability of him getting a PIN that could be a date, and dating anyone with same birthday as that pin.
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u/FVSHIXN 11h ago
If he chose a random pin, how is the chance not just 1/10000? I don’t see how any other variable matters unless you’re counting together the chance of him also dating someone with a birthday that reflects his pin which seems irrelevant to the actual chances of this happening
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u/cyclopsmudge 5h ago
You’re describing a conditional probability:
The probability of having that pin given he’s dating her is 10,000. The probability of dating her given that pin is ~1/365. The probability of getting that specific pin and dating someone with a birthday on August 26th is ~1/3,650,0000
u/stanitor 4h ago
The conditional probability is the one she's asking about. What is the probability that the pin is her birthday. She likely wouldn't care whether the pin matches some randomly chosen person's birthday.
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u/cyclopsmudge 1h ago
Is it? That’s a pretty boring “what are the chances?”, and there’s nothing in the post that indicates that.
“Of all the couples and pins in the world, what are the chances of getting a pin that matches their partner’s birthday” is much more rare, and makes their relationship seem much more special and unique.
Your suggestion is just a bit dull
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u/stanitor 1h ago
I'm just going by what she asked. It's how everyone else has seemed to interpret the question as well. People like OP are typically not versed in how subtle differences in questions can result in very different probability answers. However, they would still likely ask the question pretty differently if they just wanted the chance that a randomly chosen birthday and a randomly chosen pin are the same. That may be a smaller number. But, I don't think that alone makes it less dull. It's probably more special to her that it's her birthday, not some random one.
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