nrich 4311
'Two's company' win if the two blue balls touch each other
as well as the very helpful recording sheet, simulation results and a value for the experimental probability are given
you can keep accumulating 100s of runs
nrich 4313
'Cosy corner' win if at least one of the red balls is in any one of the three corner positions
students could be asked to estimate the probabilities after a short run experiment
theoretical probabilities for both of these simulation 'experiments' can be worked out but are not too easy to calculate (they are given, so could be quoted: 4/7 = 0.571 for 'two's company' and 57/60 = 0.95 for 'cosy corner')
NRich have a further probability experiment - equivalent to throwing two coins (4304) -a win is if both 'coins' show the same value. This can be a useful experiment to undertake since some students think there are three outcomes (both heads, both tails and one of each) so, mistakenly, think the probability of two the same is 2/3
it can also be interesting to explore the length of runs of wins or loses - maybe calculating an average length
NRich do a good copy of the (Geoff Giles) recording sheet - which has many benefits, especially in showing how results tend towards a certain value for a long run experiment
It's probably better to print the NRich student recording sheet (pdf) but here are two (ping) versions, for 50 trials:
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