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Fair Game Design Worksheet

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Fair Game Design Worksheet

Use the game data to judge fairness, explain your reasoning and improve the design. A fair game gives each player an equal chance to win. Show calculations where useful.

The Harbour Fair Challenge

Kacper and Aisling are testing games for a community fair. They record results from 20 spins of a two-colour spinner. Their first spinner has a red sector taking 12 of 20 equal sections and a blue sector taking 8 of 20.

1.What fraction of the spinner is red? Write the fraction in simplest form.

2.Which colour is more likely to be spun? How many more of its sectors are there?

3.Kacper says, “The spinner is fair because it has only two colours.” Is her reasoning correct? Explain using the sector counts.

Checking the results

They spin the spinner 20 times and record: red, blue, red, red, blue, red, blue, red, red, blue, red, blue, red, red, blue, red, blue, red, red, blue.

4.Count the results. How many reds and how many blues did they record?

5.Compare the experimental results with the spinner sectors. What do you notice?

Redesign a fair game

For the final game, a player wins a point by spinning red and the other player wins a point by spinning blue. The team wants neither player to have an advantage.

6.How many of the 20 sectors should be red, and how many should be blue, for an equally likely chance of each colour?

7.The team changes the spinner to 10 red and 10 blue sectors. What is the probability of spinning blue? Give the answer as a fraction and a percentage.

8.A different game uses a fair six-sided die. Seán wins on 1, 2 or 3; Darragh wins on 4, 5 or 6. Is this game fair? Give each player's probability of winning.

9.Design one rule change that would make the original 12-red, 8-blue spinner game fair for two players. Explain why your change gives equal chances.

10.Write a short claim about what makes a chance game fair. Support it with one piece of evidence from this worksheet.