A spinner game
Colour the equal sectors of a spinner red, blue and green, and work out the chance of landing on each colour and how many reds to expect in 60 spins. Then make the game fair.
Core concept
On a spinner with equal sectors, P(colour) = sectors of that colour ÷ all sectors; the probabilities add up to 1, and the expected number of times = probability × number of spins
Topic: Maths in everyday life
A spinner split into equal sectors is equally likely to stop on any sector. So the chance, or probability: How likely something is to happen, from 0 (impossible) to 1 (certain). All key words, of landing on a colour is the number of sectors of that colour divided by the number of sectors in all. With 3 red, 2 blue and 1 green sector, P(red) = 3 ÷ 6 = 0.5. The probabilities of all the colours add up to 1, because the spinner must land somewhere. Probability also tells us what to expect: spin 60 times and you expect red about 0.5 × 60 = 30 times. You will not get exactly 30 every time, but the more you spin, the closer you get. A game is fair when every player's colour has the same probability.
What you will learn
- Find the probability of an outcome when all outcomes are equally likely.
- Check that the probabilities of all outcomes add up to 1.
- Predict how often an outcome will happen, and make a game fair.
Before you start
- Know how to write a fraction as a decimal.
Materials
- A paper circle, a pencil and a paper clip to make a spinner
Equipment
- Colour pencils
Procedure
- Record the starting spinner: 3 red, 2 blue and 1 green.
- Make 1 red, 2 blue and 1 green, and record.
- Make one sector of each colour, and record.
How this simulation is simplified
- All the sectors are the same size and the spinner is equally likely to stop on any of them.