Najwa and Zuki play a game.

They put two red and four blue ribbons in a box. They pull out two ribbons at the same time without looking at the colours.

Najwa wins if both ribbons are the same colour.

Zuki wins if the two ribbons are different colours.

You could play the game. Make ribbons from coloured strips of paper, and put them in a bag or box so players can take one strip without seeing what colour they are taking.

Who wins more often? Is this a fair game? If not, why is it unfair?

List all the different possible events that can happen each time you play this game, for example (red and red) …

Now suppose that you change the game so that there are two red and four blue ribbons in the box?

Is this a fair game? Why or why not?

Also see www.nrich.maths.org/919

### 12 Responses to In a Box

1. Zoe says:

This was not a fair game,I would put the same number of ribbons i.e four red and four blue ribbons so that the have equal chances of winning the game.

• toni says:

Be VERY careful. With two of each colour R1, R2, B1 and B2 the choices are:
–>R1 R2 or R1 B1 or R1 B2
or R2 B1 or R2 B2
or B1 B2
Now look closely.
Only 2 choices are the same colour.
But 4 choices are different colours.
THIS IS NOT A FAIR GAME

2. Dane says:

It is not a fair game seeing as the probability that it will be the same color is 14/30 and different colors 16/30. If we wanted to make it a fair game we had to have the same amount of red ones as blue ones. Am I correct in my reasoning?

• toni says:

Look again at how you worked out those probabilities.

You are working on the right lines but having the same number of ribbons of each colour will not make it a fair game. See my reply above.

3. Mvellie says:

This is an unfair game because the chances are not equal.There must be fifty chances of winning a game.

4. Bheki says:

This kind of question will be suitable to introduce probability as it would allow learners to talk using a mathematical language and developing rules of their own. I think it would be more nicer if i use different sweets instead of a ribbon as the learners will be talking about words like unfair and fair.

• toni says:

That’s a good idea. They will really care about who wins if they get the sweets. Children naturally use the language of fair and unfair.

5. Judith says:

This is not a fair game because the players do not have equal chance of winning.

6. Godwin says:

It is not a fair game because when one ribbon is taken out it is not being replaced. Zuki has a 16/30 chances of winning the game whereas Najwa has a chance of 14/30 chance of winning the game. It is giving Zuki an unfair advantage.

7. Kgaogelo says:

It is not fair , since Najwa is 7/15 and Zuki is 8/15 the game must be fair if there is equal chances of winning