New
New
Checking and securing calculating probabilities from tables
I can calculate probabilities from tables and two-way tables.
Lesson 5 of 18
New
New
- Year 11
Checking and securing calculating probabilities from tables
I can calculate probabilities from tables and two-way tables.
Lesson details
Key learning points
- The probability of an outcome can be found by considering a table
- The probability of an event can be found by considering a table showing all possible outcomes
- The probability of an outcome can be found by considering a two-way table showing all possible outcomes for two events
- The probability of an event can be found by considering a two-way table showing all possible outcomes for two events
Keywords
Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals etc.) with some specific property.
Common misconception
Pupils may get confused between two-way tables that show outcomes and two-way tables that show frequencies (particularly when the outcomes are numbers, such as the sum of two dice rolls).
Two-way tables can be either used to display the sample space of individual outcomes or the frequencies of outcomes. Therefore, when using a table, it can be helpful to note down what type of data the table shows.
Aspects of the lesson can be made practical by asking pupils to collect data themselves that could then be organised into a two-way table. They can then calculate probabilities from their own data.
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
Loading...
Prior knowledge starter quiz
6 Questions
Q1.Here are three decks of cards.
A single card from each of Deck 1, Deck 2, and Deck 3 is drawn to make a trio.
What is the probability that this trio of cards contains a square number?
Here are three decks of cards.
A single card from each of Deck 1, Deck 2, and Deck 3 is drawn to make a trio.
What is the probability that this trio of cards contains a square number?
$$\frac{1}{6}$$
$$\frac{3}{7}$$
$$\frac{5}{8}$$
$$\frac{2}{3}$$
Correct answer: $$\frac{5}{6}$$
$$\frac{5}{6}$$
Q2.Sam plays a video game that can either be won or lost.
The probability that Sam wins the video game is 0.42.
The probability that Sam loses the video game is .
Sam plays a video game that can either be won or lost.
The probability that Sam wins the video game is 0.42.
The probability that Sam loses the video game is .
Correct Answer: 0.58
0.58
Q3.This table shows the mutually exclusive and exhaustive set of outcomes, and the probability of each outcome, from spinning a spinner once.
The value of $$x$$ is .
This table shows the mutually exclusive and exhaustive set of outcomes, and the probability of each outcome, from spinning a spinner once.
The value of $$x$$ is .
Correct Answer: 0.33
0.33
Q4.Which of these statements are correct for this frequency tree?
Which of these statements are correct for this frequency tree?
$$x$$ is equal to $$y$$
Correct answer: $$y$$ = 400
$$y$$ = 400
$$y$$ = 600
$$z$$ = 150
Correct answer: $$z$$ = 250
$$z$$ = 250
Q5.Each card on a deck of 7 cards has a unique integer written on it. A = {factors of 6}, B = {numbers ≥ 6}.
What positive integer could be on the seventh card for events A and B to not be exhaustive?
Each card on a deck of 7 cards has a unique integer written on it. A = {factors of 6}, B = {numbers ≥ 6}.
What positive integer could be on the seventh card for events A and B to not be exhaustive?
0
Correct answer: 4
4
Correct answer: 5
5
7
12
Q6.A game can either be won by either Alex, Sam, or Jacob.
P(Sam wins) = .
A game can either be won by either Alex, Sam, or Jacob.
P(Sam wins) = .
Correct Answer: 0.4
0.4
Assessment exit quiz
6 Questions
Q1.Students were asked whether they walked to school or used other transport methods, and how long their journey took them. Find the probability a student had a journey of over 15 minutes.
Students were asked whether they walked to school or used other transport methods, and how long their journey took them. Find the probability a student had a journey of over 15 minutes.
$$\frac {3}{10}$$
$$\frac {2}{3}$$
Correct answer: $$\frac {7}{10}$$
$$\frac {7}{10}$$
$$\frac {3}{4}$$
Q2.A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(multiple of 10).
A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(multiple of 10).
$$\frac{3}{36}$$
Correct answer: $$\frac{6}{36}$$
$$\frac{6}{36}$$
$$\frac{1}{12}$$
Correct answer: $$\frac{1}{6}$$
$$\frac{1}{6}$$
$$\frac{1}{2}$$
Q3.A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(not a prime number).
A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(not a prime number).
$$\frac{24}{36}$$
Correct answer: $$\frac{25}{36}$$
$$\frac{25}{36}$$
$$\frac{5}{6}$$
$$\frac{2}{3}$$
Q4.People at a bus station were surveyed their age and where their destination was.
Match each frequency from the table to its value.
People at a bus station were surveyed their age and where their destination was.
Match each frequency from the table to its value.
Correct Answer:$$a$$,181
$$a$$ - 181
Correct Answer:$$b$$,144
$$b$$ - 144
Correct Answer:$$c$$,70
$$c$$ - 70
Correct Answer:$$d$$,20
$$d$$ - 20
Correct Answer:$$e$$,270
$$e$$ - 270
Correct Answer:$$f$$,230
$$f$$ - 230
Q5.People at a bus station were surveyed their age and where their destination was.
A person is chosen at random.
Find P(60 or over and going to Rowanwood).
People at a bus station were surveyed their age and where their destination was.
A person is chosen at random.
Find P(60 or over and going to Rowanwood).
$$\frac{29}{173}$$
Correct answer: $$\frac{29}{500}$$
$$\frac{29}{500}$$
$$\frac{173}{500}$$
$$\frac{144}{500}$$
$$\frac{144}{173}$$
Q6.People at a bus station were surveyed their age and where their destination was.
A person going to Oakfield is chosen at random.
Find P(under 60).
People at a bus station were surveyed their age and where their destination was.
A person going to Oakfield is chosen at random.
Find P(under 60).
$$\frac{181}{500}$$
$$\frac{181}{257}$$
$$\frac{76}{500}$$
Correct answer: $$\frac{76}{257}$$
$$\frac{76}{257}$$
$$\frac{76}{181}$$
