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Lesson 3 of 13
  • Year 9

Calculating theoretical probabilities from lists (one event)

I can find theoretical probabilities from a list of possible outcomes for one event.

View unit
Lesson 3 of 13
New
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  • Year 9

Calculating theoretical probabilities from lists (one event)

I can find theoretical probabilities from a list of possible outcomes for one event.

Lesson details

Key learning points

  1. The probability of an outcome can be found by considering the list of all possible outcomes.
  2. The probability of a set of outcomes can be found by considering the list of all possible outcomes.
  3. A list of all possible outcomes can help us find a probability, even when the outcomes are not equally likely.

Keywords

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

Common misconception

Pupils may assume that theoretical probabilities can be also found in cases where individual outcomes are not equally likely (e.g. picking a sweet out of a box where the sweets are different shapes).

If the sweets in a box are different shapes then picking a sweet out of the box is not necessarily random. Someone could find their favourite flavour sweet by feeling the different shapes.


To help you plan your year 9 maths lesson on: Calculating theoretical probabilities from lists (one event), download all teaching resources for free and adapt to suit your pupils' needs...

Question 2 in Task B contains a link to a Desmos file. If pupils have access to a web browser, they could use to link to explore the results from multiple experiments. If not then the teacher could display the simulations on the screen or print off some of the results in advance.
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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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.
Which letter on the probability scale represents a probability of 0.5?

An image in a quiz
A
B
Correct answer: C
D
E

Q3.
The spinner is divided into equal-sized sectors. What fraction of the spinner is labelled 'win'?

An image in a quiz
$${1}\over{2}$$
$${1}\over{3}$$
$${2}\over{3}$$
Correct answer: $${2}\over{5}$$

Q4.
The spinner is divided into equal-sized sectors. % of the spinner is labelled 'lose'.

An image in a quiz
Correct Answer: 60, sixty, 60%

Q5.
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

Q6.
The probability on an outcome is 25%. Approximately how many times could you expect the outcome to occur in 500 trials?

25
50
100
Correct answer: 125
250

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
__________ probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

An experimental
An exact
A likelihood
Correct answer: A theoretical

Q2.
What is the probability that this spinner lands on 'A'?

An image in a quiz
$${1}\over{2}$$
$${1}\over{3}$$
Correct answer: $${1}\over{4}$$
$${1}\over{5}$$

Q3.
What is the probability that this spinner lands on 'win'?

An image in a quiz
$${1}\over{2}$$
$${1}\over{3}$$
$${3}\over{4}$$
Correct answer: $${3}\over{7}$$

Q4.
A counter is picked at random from the bag. What is the probability that it contains the letter B?

An image in a quiz
$${1}\over{2}$$
$${1}\over{3}$$
$${3}\over{5}$$
Correct answer: $${3}\over{8}$$

Q5.
A regular six-sided dice is rolled. What is the probability of rolling a 4?

$${1}\over{2}$$
$${1}\over{4}$$
$${1}\over{5}$$
Correct answer: $${1}\over{6}$$
$${4}\over{6}$$

Q6.
A regular six-sided dice is rolled. Which event has a probability of $${4}\over{6}$$?

rolling a cube number
rolling an even number
Correct answer: rolling a factor of 6
rolling a prime number
rolling a square number