Odds and evens

Are these games fair? How can you tell?

Problem

Odds and Evens printable sheet

 

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

 

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5 balls, each with one of the numbers 2, 3, 4, 5, 6.

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

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The balls with a 4 and 5 are chosen.

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:

 

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Set B has 5 balls, numbered 1, 3, 5, 6, 7. Set C has 6 balls numbered 2, 3, 4, 5, 6, 8. Set D has 6 balls numbered 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.

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.