THE SPINNER PROBLEM

The Barker Brothers Toy Company needs your help in designing their latest new game. Here's how it looks:

First player's
spinner
Second player's
spinner

Spinner Game Rules:
• Each player spins a spinner
• The player with the higher number on his or her spinner wins
• You may use any of the numbers
0, 2, 4, 6, 8, or 9
• You may use 2, 3, 4, 5, or 6 spaces on your spinner

Your job is to design the second player's spinner. Your spinner should be "fair". This means that the player using your spinner has an equal chance of winning as the player using the other spinner. Here's how you decide if your spinner is fair: Suppose you chose to put the numbers 0, 2, and 4 on your spinner, like this:

The possible scores against the other spinner's scores is this:

There are 3 x 4 = 12 possible combinations of your spinner's score against the other spinner's score, and your spinner only wins 3 of the 12 combinations. So your player will probably lose. It isn't fair!!. Design one where your spinner wins exactly half of the time. This makes it fair.

Your response should be on the "GAME PROBLEM RESPONSE" page:
• Part 1: Restate the problem in your own words.
• Part 2: Investigate the problem, drawing as many spinners as you can on the back of this page that fit the rules. Label the first spinner 'A', the second one 'B', and so on. Next to the spinner, write "FAIR" if you think it is fair or "UNFAIR" if not. Write sentences comparing them. Which would be more fun to play?
• Part 3: Conclusion, stating your best spinner. Explain why it is fair.
YOU HAVE 30 MINUTES TO COMPLETE THIS TASK