Do Rare Events Happen?

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.