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Lesson 12 of 13
  • Year 9

Comparing multiple representations to calculate theoretical probabilities for combined events

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

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Lesson 12 of 13
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  • Year 9

Comparing multiple representations to calculate theoretical probabilities for combined events

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

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Share activities with pupils

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Lesson details

Key learning points

  1. The probability of an outcome can be found from multiple representations.
  2. Each representation can be considered before the most appropriate is chosen.
  3. Information from one representation can be displayed using a different representation.

Keywords

  • 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.

  • 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.

Common misconception

The probability of an event is the product of the probability of each outcome in the event.

The probability of an event is the sum of the probability of each outcome in the event seen in the sample space of a diagram. For example, in the sample space at the end of a probability tree, or by adding the outcomes in the sample space of a table.


To help you plan your year 9 maths lesson on: Comparing multiple representations to calculate theoretical probabilities for combined events, 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.
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Licence

This content is © 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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6 Questions

Q1.
The that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Correct Answer: probability

Q2.
A trial has three possible outcomes: {A, B, C}. P(A) = $${2}\over{7}$$. P(B) = $${1}\over{7}$$. P(C) = $${4}\over{7}$$. Which outcome is most likely to happen?

A
B
Correct answer: C

Q3.
There are two trials. In Trial 1, a spinner with {A, B, C} is spun twice. In Trial 2, a spinner with {B, C} is spun twice. Which statement is true?

Correct answer: The likelihood of A or C appearing in the first trial is the same.
The likelihood of A appearing in the second trial is high.
The likelihood of B appearing in both trials is more than equal chance.

Q4.
In a fair six-sided die, what is the probability of rolling a 9 and getting 'tails' in a single toss of a fair coin?

Correct Answer: 0, impossible

Q5.
A coin is flipped twice. Complete the sample space ξ = {HH, HT, , TT}

HH
HT
Correct answer: TH
TT

Q6.
When rolling a fair six sided die, which event is more likely to occur?

Correct answer: Rolling an even number
Rolling a prime number > 2
Rolling a multiple of 3

Assessment exit quiz

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6 Questions

Q1.
What is the probability of event A and C happening?

An image in a quiz
$$\frac{9}{20}$$
Correct answer: $$\frac{1}{20}$$
$$\frac{1}{5}$$
$$\frac{1}{4}$$

Q2.
What number does 'b' represent?

An image in a quiz
Correct answer: 4
5
3

Q3.
An object chosen at random is most likely to be which of the following?

An image in a quiz
from Set A but not Set B
from Set B but not Set A
From neither Set A nor Set B
Correct answer: From Set A or Set B

Q4.
If one of the events below was much less likely to occur than any others, which statement would be true?

An image in a quiz
The event must be either C, D, E, or F
The event must be either B, E or F
Correct answer: The event could be any of A, B, C, D, E or F
The event can only be D or F

Q5.
If each spinner is used once, what is the probability of the first spinner landing on 'A' and the second spinner not landing on '1'?

An image in a quiz
Correct answer: $$\frac{1}{3}$$
$$\frac{1}{6}$$
$$\frac{2}{3}$$

Q6.
For a single event, what must all possibilities sum to?

Correct answer: 1
10
5
0