I have a fun math coincidence on my family: every year the birthday for both my parents and I is on the same weekday. All of them is past February, so this is always true.
What's the probability of this happening?
Is it as simple as P(x) = 1/7*1/7*1/7 or do we take anything in consideration to properly calculate the probability? #math #mathhelp #fedihelp #probability #hivemind
It's 1/7*1/7.
What you've proposed would be the probability that all three fall on, say, Monday (or any other specified day).
You could think of it like the first birthday is "unconstrained" - it has a probably of 7/7 of falling on some day off the week. It's only the second and third birthdays that are constrained, to fall on the same DOTW as the first.
(There should be some minor corrections due to there not being an even number of weeks in a year, but that should be small.)
π!
I think this is a much harder problem than that. It's necessary to account for the fact that for the situation to stay stable all three birthdays must be after February. No matter whether we have a leap year or not there are 306 days after February.
So each person has 306 ways to be born after February. The problem is that the denominator changes in a leap year and I'm not sure how to account for that, so let p be the probability that all three are born after February.
Next we want all three to be born on the same day of the week. It's easier to do this by calculating the chance that all three are born on different days. This is (7/7)(6/7)(5/7)β0.612. So the probability that all three are born on same day of week is β1-0.612=0.388.
This means the probability for the whole thing is βpΓ0.388. But what's p? I have no idea. You'd probably get a pretty decent approximation by just forgetting about leap days if that's good enough.
Disclaimer: discrete probability problems are hard and I only thought about this superficially so I wouldn't be surprised if I'm totally wrong.
All of these birthdays were after February.
"Next we want all three to be born on the same day of the week"
this is not the case, all of us were born on different days of the week!
I've checked and it works a little bit like this:
As long the weekday match on the second person birthday and third it will be true.
e.g. Person's 1 birthday on 1971 when the second person was born both were on a Thursday, and then the same happening on 1999, both parents in sync already.
I thought you were asking for the probability that all three people's birthdays would be on the same day of the week every year. For that to be true you need to include the probability that all three were born after February.
If all you're looking for is the probability that the three were born on the same day of the week only in their birth year then you're right that it's (1/7)(1/7).
Also, I was totally off my head with my complement calculation. What I calculated was the chance that at least two were born on the same day.
@AdrianRiskin This is why I always struggled with Probability: you need to describe in natural language what you really want to calculate π .
I wanted to know the odds of 3 people sharing their birthday weekday, being born after february.
In my particular case:
- all 3 born after february
- born in different days of the week, but all sync up in the eldest on the year of birth.
- we are in sync since then and will never be off-sync (unless someone dictates August 32nd π)
@tiago @AdrianRiskin
It works out the same though, right, because it's the probability that, in the year when the second person was born, the weekday of their birthday is the same as that of the oldest person, and then again for the youngest person in their year of birth. So it's still roughly 1/7 * 1/7.
Besides needing to be born after February, the reason it's not quite this simple is because there isn't exactly a 1/7th probability of being born on each day of the week, because the 306 days after February is not a multiple of 7, so there aren't the same number of ways to be born on each day of the week.
tiago 
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Adrian Riskin 
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