# Odds or Sixes?

Tania and Derek are playing a game with a dice.

They roll the dice. If the number is odd, Tania wins that round.

If the number is a six, Derek wins.

(It doesn't matter who throws the die.)

Who is more likely to win the game? Why? How could you make the game fair?

What numbers are possible to throw on the dice? Who would win with each number? Can you use this to decide how to make the game fair?

Congratulations to all of you who sent in a correct answer to this problem. There were too many of you to name all of you here, but well done! The first correct answer was sent in by Natasha and Nataneil:

Derek's chance is 1 in 6 whereas Tania's chance is 3 in 6 which gives Tania a bigger chance to win.

This is because there are 6 numbers on a die and Derek has only chosen 1, and because Tania has chosen 3 she has a bigger probability to win!!!

To make the game fair one person should have all the odd numbers and the other person have all the even numbers.

I wonder if there are some other ways of playing a fair game?

**Why do this problem?**

### Possible approach

You could introduce this problem either by having two children come to the front to play it. Whichever way you choose, play the game a few times and record the outcomes on the board. Ask the class to predict what would happen if the game was played many times, for example $100$ times. Take suggestions from the children, looking out for those who justify their answer based on the few games which have already been played.

### Key questions

### Possible extension

### Possible support