New
New
Set notation
I can use formal language for set notation and see how it relates to various representations.
Lesson 9 of 18
New
New
- Year 11
Set notation
I can use formal language for set notation and see how it relates to various representations.
Lesson details
Key learning points
- Set notation is a shorter way of writing probability statements
- The notation relates to certain aspects of a probability tree
- The notation relates to certain aspects of a two-way table
- The notation relates to certain aspects of a Venn diagram
- 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 (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
6 Questions
Q1.In which of these situations is it not possible to work out a theoretical probability?
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
Predicting the winner in a game of tennis
Correct answer: Predicting which way up a toy brick lands
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 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?
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 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.
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?
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?
Experiment 1
Experiment 2
Correct answer: Experiment 3
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 .
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 .
Correct Answer: 150
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.
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.
17
Correct answer: 34
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).
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).
Correct Answer: 0.6665
0.6665
Assessment exit quiz
6 Questions
Q1.Which symbol is used to represent the universal set?
Which symbol is used to represent the universal set?
A
A'
Correct answer: ξ
ξ
∪
∩
Q2.What does this symbol represent: ∩ ?
What does this symbol represent: ∩ ?
complement
element
Correct answer: intersection
intersection
union
universal set
Q3.What region is shown shaded in this Venn diagram?
What region is shown shaded in this Venn diagram?
A' ∪ B
A' ∩ B'
Correct answer: A' ∪ B'
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).
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: $$\frac{4}{12}$$
$$\frac{4}{12}$$
$$\frac{5}{12}$$
$$\frac{6}{12}$$
$$\frac{7}{12}$$
Q5.Which combination of events is highlighted in the tree diagram?
Which combination of events is highlighted in the tree diagram?
A ∪ B'
A' ∪ B
A' ∩ B'
Correct answer: A ∩ B'
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).
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).
Correct Answer: 0.9
0.9
