Chance and probability · Usually met around P3
Fair and unfair games
Count each player's winning outcomes: equal is fair.
How to do it
Method
Count each player's winning outcomes: equal is fair
Dice: 3 odd, 3 even: fair
Another way
Imagine many games
60 games: about 30 each when fair
In full
A game is fair when every player has the same chance of winning. Count the outcomes each player wins on: the same number means fair; different numbers mean unfair, and the one with more is likelier to win. With a dice, odd for A and even for B gives each 3 outcomes: fair. 1 or 2 for A and the rest for B is 2 against 4: unfair. To make it fair, change the rule so both have the same number of outcomes, or change the spinner or the balls in the bag; an outcome where you spin or roll again belongs to nobody and isn't counted. Or imagine playing many times: in a fair game both players win about as often.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Tsz-ching and Ka-lok spin this spinner: red 🔴 and Tsz-ching wins; blue 🔵 and Ka-lok wins. The game is fair.
True or false?
Show the answer and working
Answer: False
The parts are equal: 4 red, 2 blue. Only equal numbers give both the same chance.
Example 2
Chi-keung and Ka-lok take a ball from this bag: red 🔴 and Chi-keung wins, blue 🔵 and Ka-lok wins. What is the fewest balls to put in to make the game fair?
Show the answer and working
Answer: 3
4 red and 1 blue. Fair needs equal numbers: put 3 into the colour with fewer.
Example 3
Tsz-hin and Ka-yee spin this spinner: red 🔴 and Tsz-hin wins, blue 🔵 and Ka-yee wins. What is the fewest red parts to repaint blue to make the game fair?
Show the answer and working
Answer: 4
10 parts, so fair means 5 red and 5 blue. There are 9 red: repaint 9 − 5 = 4.
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