•The probability of winning is 1/20.
© MEI 2009
Teachers’ notes
Links to tree diagrams or systematic listing of possible outcomes.
•
•
The question could be simplified to 4 squares, 2 of which have identical
amounts behind them. Scratch off 2 squares, what is the probability of
winning?
Approaches to getting an answer include:
– Using a tree diagram
– Systematic finding of possibilities
These are shown on the next two pages.
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Follow up questions include
– What if there were 8 squares, 4 of them hiding the same amount, and you had to
scratch off 4 squares. What is the probability of winning?
– The probability of winning any prize is 1/20. The possible prizes are £1, £10, £20
or £100. Do you think they are equally likely or could some prizes be more
common? What would be a fair price for the card if each prize came up just as
much as the others? (i.e. There is a 1/20 chance of winning a prize and, if you
win a prize, it is equally likely to be £1 or £10 or £20 or £100 so the probability of
winning each prize is 1/80 and the probability of winning nothing is 19/20.)
© MEI 2009
Using a tree diagram to find the probability of getting the 3
amounts that are the same
3 2 1 1
P(Win) = × × =
6 5 4 20
© MEI 2009
Using systematic listing to find the probability of
getting the 3 amounts that are the same
The 3 squares scratched off could be in any of the following positions:
Etc. There are 20 possible selections of 3
squares. Only one of these will win.
© MEI 2009