Starter quiz
- In which of these situations is it not possible to work out a theoretical probability?
- Predicting the winner in a game of tennis ✓
- Predicting which way up a toy brick lands ✓
- Predicting the outcome of flipping a fair coin
- Predicting the winner in a race ✓
- Predicting the outcome of spinning a fair spinner
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- Izzy rolls a die 4 times. The dice lands on a '6' three times. Which of these statements are correct?
- 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.
- The die could be biased but more trials are needed to be sure. ✓
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- 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
- Experiment 3 ✓
- Experiment 4
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- 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 ______.
- '150' ✓
- 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
- 34 ✓
- 51
- 68
- 126
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- 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).
- '0.6665' ✓
Exit quiz
- Which symbol is used to represent the universal set?
- A
- A'
- ξ ✓
- ∪
- ∩
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- What does this symbol represent: ∩ ?
- complement
- element
- intersection ✓
- union
- universal set
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- What region is shown shaded in this Venn diagram?
- A' ∪ B
- A' ∩ B'
- A' ∪ B' ✓
- A ∪ B
- A ∪ B'
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- 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).
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- ✓
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- Which combination of events is highlighted in the tree diagram?
- A ∪ B'
- A' ∪ B
- A' ∩ B'
- A ∩ B' ✓
- A' ∩ B
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- 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).
- '0.9' ✓
Worksheet
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Presentation
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Video
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
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.
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.
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