I celebrate my birthday on the same day as one of my grandchildren. Just wonder how rare it would be for three people in the same family to celebrate their birthdays on the same day.
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6$\begingroup$ That depends on how many people are in the family. $\endgroup$– DanMay 13 at 22:09
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1$\begingroup$ Not as rare as you might initially think. $\endgroup$– DanMay 13 at 22:13
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1 Answer
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Let's work out for a family of four, $A,B,C,D$
So three share the same birthday, and one person is the odd person out.
- There are $4$ possible odd-person-out.
- This person could have any birthday, and $364$ days are left for the trio to share one in common, ignoring leap years
Thus $Pr = 4\times \frac{364}{365}(\frac{1}{365})^2, \approx\dfrac{1}{33398}$
answered May 14 at 7:31