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Lesson 9 of 13
  • Year 9

Calculating theoretical probabilities from two-way tables (two events)

I can calculate and use theoretical probabilities for combined events using two-way tables (2 events).

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View unit
Lesson 9 of 13
New
New
  • Year 9

Calculating theoretical probabilities from two-way tables (two events)

I can calculate and use theoretical probabilities for combined events using two-way tables (2 events).

Download all

These resources were made for remote use during the pandemic, not classroom teaching.

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Lesson details

Key learning points

  1. The probability of an outcome can be found by considering a two-way table showing all possible outcomes for two events.
  2. The probability of a set of outcomes can be found using a two-way table showing all possible outcomes for two events.
  3. The probability of a set of outcomes can be found using a two-way table, even when the outcomes are not equally likely.

Keywords

  • Theoretical probability - 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 struggle with finding the probability of A or B, and may count the outcomes that belong to A and B twice.

If you use an example, such as visiting particular countries, ask the pupils how someone would respond to the question 'have you visited X or Y' if they have in fact visited both countries.


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

If pupils have a copy of the table, potentially on a mini whiteboard, they can circle the outcomes/regions of the table that satisfy the combined events, before calculating the probability.
Teacher tip

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.
In a fair six-sided die, what is the probability of rolling a 5 and getting a head in a single toss of a fair coin?

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

Q2.
A counter is taken from the bag. Its letter is noted and then it is placed back into the bag. A counter is taken from the bag again. Which of these options is not the correct sample space?

An image in a quiz
ξ = {AA, AB, AC, BA, BB, BC, CA, CB, CC}
Correct answer: ξ = {AA, AB, BA, BB, BC, CA, CB, CC}

Q3.
If the probability of an event (A) is $$/frac{3}{7}$$, and the experiment is repeated 49 times, what is the theoretical number of times event (A) will occur?

3
7
Correct answer: 21
49

Q4.
Which of the events {A,B,C} is the least likely to occur according to this probability tree?

An image in a quiz
Correct answer: A
B
C
None.

Q5.
John uses an unbiased random selection tool to generate a single letter of the alphabet. It is repeated three times. Which of the following letter sequences is the least likely?

A,G,H
A,A,A
M,O,O
B,I,N
Correct answer: All selections are equally likely

Q6.
There are two trials. In Trial 1, a spinner with {A, B} is spun twice. In Trial 2, a spinner with {B, C} is spun twice. Which statement is true?

The total number of possible outcomes in Trial 1 is greater than in Trial 2.
The total number of possible outcomes in Trial 1 is less than in Trial 2.
Correct answer: The total number of possible outcomes in Trial 1 is the same are in Trial 2.

Assessment exit quiz

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6 Questions

Q1.
If this spinner is spun twice, what is the probability that the sum of both results would be 11?

An image in a quiz
$$\frac{1}{32}$$
$$\frac{1}{64}$$
Correct answer: $$\frac{1}{16}$$
$$\frac{11}{64}$$

Q2.
If this spinner is spun twice, what is the probability of not losing either time?

An image in a quiz
$$\frac{1}{9}$$
$$\frac{1}{3}$$
$$\frac{2}{9}$$
Correct answer: $$\frac{4}{9}$$

Q3.
If this spinner is spun twice, what is the probability that the sum of both results would be odd?

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

Q4.
If spun twice what is the probability this spinner would spell 'pea' then 'nut' ?

An image in a quiz
$$\frac{1}{5}$$
$$\frac{1}{25}$$
$$\frac{2}{5}$$

Q5.
If each of these spinners is spun once, what is the probability of getting H and 6?

An image in a quiz
$$\frac{1}{10}$$
$$\frac{1}{5}$$
Correct answer: 0

Q6.
If this spinner is spun twice, what is the probability of the sum of the results being less than 10?

An image in a quiz
Correct answer: $$\frac{19}{64}$$
$$\frac{23}{64}$$
$$\frac{17}{64}$$