Same or different?
Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.
Problem
Anna and Becky were playing a game. They put one purple cube and two yellow cubes into a bag.
First Anna picked a cube out of the bag without looking, then Becky picked one out.
If the two cubes the girls picked out were the same colour, Anna won the game. If they picked out two differently coloured cubes, then Becky was the the winner.
Is this a fair game?
Explain your answer.
Thank you to Doug Williams from the Mathematics Task Centre Project for this problem. If you'd like to take this idea a bit further, look at In a Box.
Getting Started
Try playing the game a large number of times (e.g. $30$ or more) with a friend and record who wins each time. You could do this at school and ask members of your class to play five games in pairs, then gather all the results together. Did someone seem to win more often?
If the first cube drawn out of the bag is purple, what is the chance that the next one is the same? Or different?
What about if the first cube is yellow?
Student Solutions
Simone sent us her work on this problem:
Well done, Simone. I wonder how you know that all three of the possibilities are equally likely?
Teachers' Resources
Same or Different?
Anna and Becky were playing a game. They put one purple cube and two yellow cubes into a bag.
First Anna picked a cube out of the bag without looking, then Becky picked one out.
If the two cubes the girls picked out were the same colour, Anna won the game. If they picked out two differently coloured cubes, then Becky was the the winner.
Is this a fair game?
Explain your answer.
Thank you to Doug Williams from the Mathematics Task Centre Project for this problem. If you'd like to take this idea a bit further, look at In a Box.
Why do this problem?
Possible approach
Key questions
Possible extension
Possible support