Spinners

Introduction

In this lesson, we will further explore combined events through probability spinners.

Part 1

  1. Draw sample space diagrams If I add the numbers up of:

  • Two 6-sided spinners

  • Two 5-sided spinners

  • A 5-sided spinner with a 6-sided spinner

  1. For each of the above, find the probability of getting:

  • A prime number

  • Not a square number

  • An odd number and a triangular number

  • A multiple of 5 or a greater than 10

Part 2

  1. Now add the following information to your sample space diagrams in Q1:

  • For the 6-sided spinners: 1, 2, 3 are red; 4, 5 are blue and 6 is yellow

  • For the 5-sided spinners: 1, 2 are red; 3, 4 are blue and 5 is green

  1. For each of the three combinations of spinners in Q1, find the probability of getting the following colours when you mix the colours up (Hint: you may wish to Google mixing primary and secondary colours):

  • Red

  • Blue

  • Yellow

  • Green

  • Orange

  • Violet

  • Cyan

  • Brown

  1. Which other colour can be found but is missing from above?

  2. To work out the probabilities above, one way is determine what proportions of your sample space diagrams are shaded those colours? Can you think of another way of working this out by manipulating fractions of the original colours?

  3. What is the benefit of this approach?

Further Questions and Challenges

The benefit of the approach mentioned at the end of last section can be illustrated below.

What if we now have three 6-sided spinners? For each spinner, 1, 2, 3 are red; 4, 5 are blue and 6 is yellow. What is now the probability of getting the following colours when you mix the colours up?

  • Red

  • Blue

  • Yellow

  • Green

  • Orange

  • Violet

  • Which other colour can be found but is missing from above?

Further Practice

Some of the essential skills introduced in this lesson are listing outcomes, sample space, two way tables and probabilities of combined events. You may also wish to look at frequency trees and tree diagrams on transum. While these are skills that you will learn more about year 9, they are useful for the further questions and challenges section above. Practise these relevant skills on DrFrostMaths, CorbettMaths, MyiMaths and Eedi.

Extension

You may want to try some of these activities by Don Steward on probability sample space, experimental probability and probability of combined events.