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Simone sent us her work on this problem:

I tried playing this game with my partner at school, and he won much more often than me. He won if the colours were different, and I won if the colours were the same.
I think this is because there are three different pairs that could come out when we take the cubes out: it could be purple yellow, or yellow yellow, or yellow purple. Each one is just as likely. But Becky wins on two of these, and Anna only wins on one. So the game isn't fair.
 

Well done, Simone.  I wonder how you know that all three of the possibilities are equally likely?