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MSV 23: Balls in a Box

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

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MSV 23: Balls in a Box

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

  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. Does your calculation roughly agree with the spreadsheet result? How could we improve the agreement? 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?

  5. An apparently unrelated fact: 1 + 2 + 3 ...+ n isTn, where Tnis the nth triangle number. Can we find a formula for Tn? This diagram shows that T5 is (6x5)/2 = 15. Can you generalise this? What is Tn using this method?

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

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

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