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
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.
Work out the probability that your two balls
are the same colour.
Put your values for m and n into the boxes on the
Excel spreadsheet below, and run the simulation.
Balls in a Box
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?
An apparently unrelated fact: 1 + 2 + 3 ...+ n isTn,
where Tnis the nth triangle number.
Can we find
This diagram shows that T5 is (6x5)/2 = 15.
Can you generalise this?
What is Tn using this method?
So we have that Tn is n(n+1)/2.
This is surprisingly useful in thinking
connects m and n
in our problem!
is written by Jonny Griffiths