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Year 11
Higher

Checking and securing calculating probabilities from diagrams

I can calculate probabilities from probability trees and Venn diagrams.

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New
New
Year 11
Higher

Checking and securing calculating probabilities from diagrams

I can calculate probabilities from probability trees and Venn diagrams.

Download all resources
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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 by considering a tree diagram
  2. The probability of an event can be found by considering a tree diagram
  3. The probability of an outcome can be found by considering a Venn diagram
  4. The probability of an event can be found by considering a Venn diagram

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.

  • Exhaustive events - A set of events are exhaustive if at least one of them has to occur whenever the experiment is carried out.

  • Mutually exclusive - Two or more events are are mutually exclusive if they share no common outcome.

Common misconception

Pupils may add the probabilities along branches of a probability tree, rather than multiplying them.

Remind pupils that probabilities cannot be greater than 1 and demonstrate that adding across the branches sometimes results in a probability that is greater than 1. Therefore, it must be wrong.

Pupils could be asked to think of different ways to group together outcomes of a dice roll to create events and check that their probabilities sum to 1 (e.g. multiple of 3 and not multiple of 3). They could then draw probability trees that involve these events and calculate more probabilities.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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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 15 minutes or under.
An image in a quiz
Correct answer: $$\frac {3}{10}$$
$$\frac {1}{3}$$
$$\frac {2}{3}$$
$$\frac {7}{10}$$
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 5).
An image in a quiz
$$\frac{6}{36}$$
Correct answer: $$\frac{8}{36}$$
$$\frac{10}{36}$$
$$\frac{1}{9}$$
Correct answer: $$\frac{2}{9}$$
Q3.
A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together. Find P(prime number).
An image in a quiz
$$\frac{10}{36}$$
Correct answer: $$\frac{11}{36}$$
$$\frac{12}{36}$$
$$\frac{13}{36}$$
Q4.
People at a bus station were surveyed their age and where their destination was. Match each frequency from the table to its value.
An image in a quiz
Correct Answer:$$a$$,141

141

Correct Answer:$$b$$,84

84

Correct Answer:$$c$$,80

80

Correct Answer:$$d$$,40

40

Correct Answer:$$e$$,190

190

Correct Answer:$$f$$,210

210

Q5.
People at a bus station were surveyed their age and where their destination was. A person is chosen at random. Find P(under 60 and going to Oakfield).
An image in a quiz
$$\frac{141}{500}$$
$$\frac{141}{207}$$
$$\frac{66}{207}$$
Correct answer: $$\frac{66}{400}$$
$$\frac{66}{141}$$
Q6.
People at a bus station were surveyed their age and where their destination was. A person going to Rowanwood is chosen at random. Find P(60 or over).
An image in a quiz
$$\frac{84}{400}$$
$$\frac{84}{113}$$
$$\frac{29}{84}$$
Correct answer: $$\frac{29}{113}$$
$$\frac{29}{400}$$

Exit quiz

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6 Questions

Q1.
A set of events are if at least one of them has to occur whenever the experiment is carried out.
Correct Answer: exhaustive
Q2.
A survey asked people whether they lived in Oakfield or not, and if they last shopped by online delivery or by going in-store. A random person is selected. Match each event to its probability.
An image in a quiz
Correct Answer:P(lives in Oakfield),$$250\over400$$

$$250\over400$$

Correct Answer:P(doesn't live in Oakfield),$$150\over400$$

$$150\over400$$

Correct Answer:P(shops in-store),$$260\over400$$

$$260\over400$$

Correct Answer:P(shops online),$$140\over400$$

$$140\over400$$

Correct Answer:P(lives in Oakfield and shops online),$$100\over400$$

$$100\over400$$

Q3.
A swimming club has 80 members. There are 13 members who swim both front crawl (FC) and butterfly (BF). The value of $$x$$ is .
An image in a quiz
Correct Answer: 20
Q4.
This probability tree shows the probability of one of two events occurring. The value of $$x$$ is .
An image in a quiz
Correct Answer: 0.65
Q5.
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. Use the probability tree to find the probability that they both lose their game.
An image in a quiz
0.012
Correct answer: 0.12
0.13
0.42
0.7
Q6.
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. The probability that at least one of them loses their match is .
An image in a quiz
Correct Answer: 0.58