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
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)ā0.612. So the probability that all three are born on same day of week is ā1-0.612=0.388.
This means the probability for the whole thing is āpĆ0.388. 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.
@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 
Adrian Riskin 
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