Pick a Number

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

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.

pick a numberIn this animation, the computer simulates a number of people $N$ choosing a number at random between 1 and $(\frac{N}{2})^2$. So, for example, it will simulate 400 people choosing a number between 1 and 40000.
How often would you expect it to pick the same number twice?

If you had Flash Player you would see that 400 people could choose a number between 1 and 40000, and there would be a duplicate around 80% of the time. Very surprising! You need to install the Adobe Flash Player to see the animation.

Click to enlarge the animation

Try it and see if it matches your guess. Click on the link below to see the animation in full screen.

In What are the chances? we show that the chance of there being no match is 13% when 20 people pick numbers between 1 and 100.

In Maths of coincidence we give a general formula that shows that the chance of there being no match is 13% whenever $(N/2)^2$ pick numbers at random between $1$ and $N$, whatever the choice of $N$.

File Duplicate.swf15.17 KB