What is the probability that three living people in the same family will celebrate their birthdays on exactly the same day.

Question

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.

Answer 1

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 $Pr = 4\times \frac{364}{365}(\frac{1}{365})^2, \approx\dfrac{1}{33398}$