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Odds and Evens

Age 11 to 14
Challenge Level

Odds and Evens printable sheet
 

Here is a set of numbered balls used for a game:
 

 Set of balls: 2, 3, 4, 5, 6

To play the game, the balls are mixed up and two balls are randomly picked out together. For example:

one ball numbered 4 and one ball numbered 5

The numbers on the balls are added together: $4 + 5 = 9$

If the total is even, you win.
If the total is odd, you lose.
How can you decide whether the game is fair?

You might like to experiment with the interactivity below.
 
 

Here are three more sets of balls:
 
 Set B: 1,3,5,6,7 Set C: 2,3,4,5,6,8 Set D 1,3,4,5,7,9


Which set would you choose to play with, to maximise your chances of winning?

Click on the links below to explore each set using the interactivity.
Set B
Set C
Set D

What proportion of the time would you expect to win each game?

You may wish to look at the problem Odds and Evens Made Fair to explore whether it is possible to change the number of balls to make the game fair. 
 
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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