Monday, 11 July 2011

cereal packet problem

suppose a cereal packet manufacturer decides to put one of six Harry Potter figures inside each box:

Harry , Ron , Hermione , Dumbledore , Voldemort , Malfoy

how many boxes, on average, would it take to collect all six figures?

six is chosen because of the ease of simulation with a dice
on average it should need 14.7 'goes'
this is 6(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6), a generalisable result

a simulation from Illinois enables various numbers of animal free gits to be (all) collected:

students can use this repeatedly to estimate the number of packets that need to be bought

if you don't mind promoting a commercial product (a breakfast cereal) then there is a good simulator that plots a histogram when all are collected - showing how many of each were obtained 

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