# Coincidences

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

You bump into an old friend you haven't seen for years.
You find that you share a birthday with not just one but two other people in your office.
You win the lottery!

You remark on the coincidence of you and the old friend being in the same place at the same time, on the coincidence of three same-day births with 365 (or 366) different dates to choose from. You toast the coincidence of your choosing the same six numbers this week as the lottery machine!

All these coincidences are remarkable as they happen to you - but none are particularly newsworthy. They are surprising for the person involved - but not that remarkable when you hear they happened to someone else.

We can use the theory of probability to investigate coincidences. And some look as though they need investigating.

For example, it is very rare in the UK for a mother to die after giving birth. Yet in 2007, two mothers admitted to a hospital on the same day died within a few days of a Streptococcus A infection. Was this just a coincidence? - a terrible coincidence but nevertheless 'just one of those things'. Or was it more significant?

What we have to consider is not just the single surprising event, but also how many opportunities there have been for 'similar' events to have occurred within the same area or time. Another problem then arises, in deciding what we mean by 'similar'!

• In Why does anyone win the lottery? we look at the chance of getting that big win, and find out that there is also a 13% chance of no one getting the jackpot in any particular draw.
• In Maternal Deaths we take a closer look at those two unfortunate mothers, and the significance of their fatal coincidence
• In Three children with the same birthday? we look at a recent news story in which three children in the same family all had the same birthday, and show this is not so amazing.
• In Born in the Same Minute we consider two children in the same family, born in different years but sharing the same date and even time of birth.
• We can explore probability further in Pick a Number. Here's one you can try at home. Get a group of people to pick numbers at random. For example: get a group of 20 people to choose whole numbers between 1 and 100. You find that they rarely will all pick different numbers. You can experiment with this using the animation, then go on to look at the mathematics of it if you like.

If you want to look at some of the maths behind coincidences, start with Why coincidences happen.

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