MSV 23: Balls in a Box

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# MSV 23: Balls in a Box - PowerPoint PPT Presentation

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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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

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

http://www.s253053503.websitehome.co.uk/msv/msv-23/msv-23.xlsm

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

a formula

for Tn?

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