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# Do Rare Events Happen?

**Do you think there is a family in the UK with three children who all have the same birthday (but born in different years)?**

How rare do you think this is?

How often do you think a baby is born in the UK who shares their birthday with both their older siblings? Do you think it happens:

**Can you calculate the probability that this might happen to a particular family?**

When you've thought about this question, click on the button below:

A child is born. Later on, some siblings are born...

What is the probability that the second child is born on the same day as the first child?

What is the probability that the third child is born on the same day as the first child?

Can you combine these probabilities to find the probability that all three children are born on the same day?

**What assumptions have you made in these calculations? Do you think these assumptions are reasonable?**

**If there are 1 million families in the UK with at least three children, how many of these would you expect to have three children born on the same day?**

How does this compare with your original thoughts?

*You can read more about the probabilities on Plus or Understanding Uncertainty, and you might like to try Last One Standing.*

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 11 to 16

Challenge Level

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*This resource is part of the collection Probability and Evidence.*

How rare do you think this is?

How often do you think a baby is born in the UK who shares their birthday with both their older siblings? Do you think it happens:

- To several families per year?
- To one family per year?
- Only every few years?
- Less often?

When you've thought about this question, click on the button below:

A child is born. Later on, some siblings are born...

What is the probability that the second child is born on the same day as the first child?

What is the probability that the third child is born on the same day as the first child?

Can you combine these probabilities to find the probability that all three children are born on the same day?

How does this compare with your original thoughts?