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Lesson 7 of 13
  • Year 9

Comparing multiple representations to calculate theoretical probabilities

I can compare and contrast the usefulness of the different representations when calculating theoretical probabilities.

View unit
Lesson 7 of 13
New
New
  • Year 9

Comparing multiple representations to calculate theoretical probabilities

I can compare and contrast the usefulness of the different representations when calculating theoretical probabilities.

Lesson details

Key learning points

  1. The probability of an outcome can be calculated from each representation.
  2. Different representations show the same information in different ways.
  3. Some representations may be easier to use than others, depending on the context.

Keywords

  • Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property.

  • Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.

  • Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

  • Theoretical probability - Theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

  • Probability tree - Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

Common misconception

Venn diagrams are useful when generating a complete list of outcomes and showing the probabilities of that list.

Venn diagrams can be very useful when categorising already known outcomes into events. The Venn diagram can then be used to calculate probabilities. However, Venn diagrams are not as useful when generating a list of outcomes.


To help you plan your year 9 maths lesson on: Comparing multiple representations to calculate theoretical probabilities, download all teaching resources for free and adapt to suit your pupils' needs...

Probability trees can be used to show the probabilities of both individual and unique outcomes from a trial, as well as events from a trial, whilst outcome and frequency tables can be used to show outcomes which probabilities can be calculated from.
Teacher tip

Licence

This content is Β© Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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5 Questions

Q1.
In a fair six-sided die, what is the probability of rolling a 6 and getting a head in a single toss of a fair coin?

$$\frac{1}{6}$$
Correct answer: $$\frac{1}{12}$$
$$\frac{1}{2}$$

Q2.
What is the probability that this spinner will land on an odd number?

An image in a quiz
1
$$\frac{1}{3}$$
Correct answer: $$\frac{2}{3}$$

Q3.
What is the probability that the letter B is selected at random from this bag?

An image in a quiz
Correct answer: $$\frac{3}{8}$$
$$\frac{5}{8}$$
$$\frac{3}{4}$$

Q4.
A coin is flipped three times. Which outcome is missing from the following sample space? ΞΎ = {HHH, HHT, HTH, HTT, , THT, TTH, TTT}

Correct answer: THH
TTH
TTT
THT

Q5.
What is the probability of the spinner landing on either A or B?

An image in a quiz
Correct answer: $$/frac{1}{3}$$
$$/frac{1}{2}$$
$$/frac{1}{4}$$

Assessment exit quiz

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6 Questions

Q1.
If Set A = {𝜸, 𝜹} and Set B = {𝞡,𝜹, 𝜽}, what symbol is missing from the Venn diagram?

An image in a quiz
Correct answer: 𝞡
𝜹
𝜷

Q2.
Which of the following represents set B?

An image in a quiz
{ } (empty)
Correct answer: {β—–, β–Ά, β–‘ }
{β—–, β–Ά, β–‘, β–  }

Q3.
Which of the following represents set A?

An image in a quiz
{ } (empty)
{β—–, β–Ά, β–‘ }
Correct answer: {β—–, β–Ά, β–‘, β–  }
{ β–  }

Q4.
If set A = {2,4,7} and set B = {5}, what is the error in the diagram?

An image in a quiz
There should be no '4' in the left circle.
The '5' should be in the intersection.
Correct answer: The '7' should be in A, but not in the intersection.

Q5.
Which of the following is a correct statement about this diagram

An image in a quiz
Correct answer: There is nothing in Set B that is not in Set A
Set B is empty
Set A contains 1 object
There is nothing in Set A that is not in Set B

Q6.
Use the Venn diagram to write the probability P(only A)

An image in a quiz
$$\frac{3}{4}$$
$$0$$
Correct answer: $$\frac{1}{4}$$
$$\frac{1}{2}$$