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Dylan from Colchester Royal Grammar School said
I think this should happen to several families per year, because of the chances of people sharing a birthday.
So, the first baby to be born can have their birthday on any day of the year.
The second baby has a chance of $\frac{1}{365}$ of being born on the same day as the first.
Then, the chance of the third baby being born on the same day is $\frac{1}{365}$.
So, you have to multiply the fractions together to work out the chance of them all being born on the same day:
1 x $\frac{1}{365}$ x$\frac{1}{365}$= $\frac{1}{133225}$.
So, if there are a million families in the UK with 3 children then the chances are that roughly 7 or 8 of them have a shared birthday.
Zach also sent in his solution.
He thought about what assumptions he was making. He also considered whether it would make a difference if you specified a date for all siblings to be born on. You can see his full solution here.
Do Rare Events Happen?
Age 11 to 16
Challenge Level 
Dylan from Colchester Royal Grammar School said
I think this should happen to several families per year, because of the chances of people sharing a birthday.
So, the first baby to be born can have their birthday on any day of the year.
The second baby has a chance of $\frac{1}{365}$ of being born on the same day as the first.
Then, the chance of the third baby being born on the same day is $\frac{1}{365}$.
So, you have to multiply the fractions together to work out the chance of them all being born on the same day:
1 x $\frac{1}{365}$ x$\frac{1}{365}$= $\frac{1}{133225}$.
So, if there are a million families in the UK with 3 children then the chances are that roughly 7 or 8 of them have a shared birthday.
Zach also sent in his solution.
He thought about what assumptions he was making. He also considered whether it would make a difference if you specified a date for all siblings to be born on. You can see his full solution here.