In a box

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Problem

Image

In a Box printable sheet

Chris and Jo decide to play a game.

They put some red and some blue ribbons in a box.

They each pick a ribbon from the box without looking (and without replacing them).

Jo wins if the two ribbons are the same colour and Chris wins if the two ribbons are a different colour.

 

How many ribbons of each colour would you need in the box to make it a fair game?

Is there more than one way to make a fair game?

 

This problem is based on one offered by Doug Williams at the 2003 ATM conference in Bath UK. See also https://www.mathematicscentre.com.

 

Click here for a poster of this problem.