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Year 11
Foundation

Set notation

I can use formal language for set notation and see how it relates to various representations.

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New
New
Year 11
Foundation

Set notation

I can use formal language for set notation and see how it relates to various representations.

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. Set notation is a shorter way of writing probability statements
  2. The notation relates to certain aspects of a probability tree
  3. The notation relates to certain aspects of a two-way table
  4. The notation relates to certain aspects of a Venn diagram
  5. The notation relates to certain aspects of a frequency tree

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.

  • Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

  • Tree diagram - Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

Common misconception

Pupils may think that A ∪ B means 'to be either from A or B (but not both)'.

A ∪ B represents all members that satisfy at least one of the events A or B. So it could be from A, from B or from both A and B.

To extend pupils further, they could be asked to find different set notations that represent the same set. E.g. (A′ ∪ B′) is equivalent to (A ∩ B)′.
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.
In which of these situations is it not possible to work out a theoretical probability?
Correct answer: Predicting the winner in a game of tennis
Correct answer: Predicting which way up a toy brick lands
Predicting the outcome of flipping a fair coin
Correct answer: Predicting the winner in a race
Predicting the outcome of spinning a fair spinner
Q2.
Izzy rolls a die 4 times. The dice lands on a '6' three times. Which of these statements are correct?
Correct answer: The die could be fair but more trials are needed to be sure.
The die is definitely fair.
The die is definitely biased towards a 6.
The die is definitely not biased towards a 6.
Correct answer: The die could be biased but more trials are needed to be sure.
Q3.
A spinner contains three letters: A, B and C. The tables show results from four experiments with the spinner. Which experiment will produce the most reliable set of experimental probabilities?
An image in a quiz
Experiment 1
Experiment 2
Correct answer: Experiment 3
Experiment 4
Q4.
The table shows the theoretical probabilities of taking a counter of a specific colour out of a bag of counters. In 1000 trials, the number of times you should expect to draw a green counter is .
An image in a quiz
Correct Answer: 150
Q5.
A box contains 100 counters. A counter is drawn, its colour noted and replaced. The results are in the table. Estimate how many green counters are in the box.
An image in a quiz
17
Correct answer: 34
51
68
126
Q6.
A class investigates whether a 6-sided die is biased. The table shows the results. Estimate the probability of the die landing on a factor of 6. P(factor of 6) = (as an unrounded decimal).
An image in a quiz
Correct Answer: 0.6665

Exit quiz

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6 Questions

Q1.
Which symbol is used to represent the universal set?
A
A'
Correct answer: ξ
∪
∩
Q2.
What does this symbol represent: ∩ ?
complement
element
Correct answer: intersection
union
universal set
Q3.
What region is shown shaded in this Venn diagram?
An image in a quiz
A' ∪ B
A' ∩ B'
Correct answer: A' ∪ B'
A ∪ B
A ∪ B'
Q4.
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {multiples of 4}, B = {factors of 12}. Find P(A' ∩ B).
$$\frac{3}{12}$$
Correct answer: $$\frac{4}{12}$$
$$\frac{5}{12}$$
$$\frac{6}{12}$$
$$\frac{7}{12}$$
Q5.
Which combination of events is highlighted in the tree diagram?
An image in a quiz
A ∪ B'
A' ∪ B
A' ∩ B'
Correct answer: A ∩ B'
A' ∩ B
Q6.
Lucas and Izzy each play one game of chess that they can either win or lose. P(Lucas wins ∪ Izzy wins) = (give your answer as a decimal).
An image in a quiz
Correct Answer: 0.9