1. MSV 23: Balls in a Box www.making-statistics-vital.co.uk

2. There are m white and n black balls in a box. Pick your own values for m and n, and write them down. A ball is picked at random, and then another. (Without replacement!) Work out the probability that your two balls are the same colour.

3. Put your values for m and n into the boxes on the Excel spreadsheet below, and run the simulation. Balls in a Box Spreadsheet Hyperlink http://www.s253053503.websitehome.co.uk/ msv/msv-23/msv-23.xlsm

4. Now you are told that P(two balls are the same colour) = 0.5. What does this tell you about the values of m and n? Does your calculation roughly agree with the spreadsheet result? How could we improve the agreement?

5. An apparently unrelated fact: 1 + 2 + 3...+ n is T n, where T n is the n th triangle number. This diagram shows that T 5 is (6x5)/2 = 15. Can you generalise this? What is T n using this method? Can we find a formula for T n ?

6. So we have that T n is n(n+1)/2. This is surprisingly useful in thinking about what connects m and n in our problem!

8. www.making-statistics-vital.co.uk is written by Jonny Griffiths hello@jonny-griffiths.net