Starter quiz
- Which of these are equivalent to ?
- ✓
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- ✓
- % ✓
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- Andeep carries out the following trial: spinning this spinner once. Which of these is the sample space of distinct outcomes for Andeep's trial?
- There are 5 sectors.
- There are 4 distinct outcomes.
- {A, A, B, C, D}
- {A, B, C, D} ✓
- {A, A} is the repeated outcome.
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- Each sector in a spinner is of equal size. In which spinners are the outcomes of “win” and “lose” equally likely?
- A
- B ✓
- C ✓
- D
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- A fair, 6-sided dice has outcomes: {2, 3, 4, 5, 6, 7}. Which of these events is most likely to happen?
- multiple of 2
- multiple of 3
- even number
- prime number ✓
- square number
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- A fair 6-sided dice has outcomes: {1, 2, 3, 4, 5, 6}. Event: if the dice lands on a prime number, Aisha wins. Which of these outcome spinners most closely represents the likelihood of Aisha winning?
- A
- B
- C ✓
- D
- E
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- Trial: a spinner will be spun twice. The outcome of each spin will be multiplied together. The spinner has outcomes: {2, 5, 7, 11, 15}. Match the letters to their correct value in the outcome table.
- A⇔30 ✓
- B⇔11 ✓
- C⇔121 ✓
- D⇔10 ✓
- E⇔5 ✓
Exit quiz
- The outcome tree represents all outcomes from spinning the spinner once. Which outcomes are missing from the outcome tree?
- 3
- 6
- 9 ✓
- 12
- 14 ✓
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- The outcome tree represents all outcomes from spinning spinner P and spinner Q once each. Match each letter to its value.
- a⇔16 ✓
- b⇔27 ✓
- c⇔8 ✓
- This outcome tree represents all outcomes from spinning spinner R twice. The sample space shows the outcomes when the results of each spin are added. Match each letter to its value.
- a⇔11 ✓
- b⇔16 ✓
- c⇔13 ✓
- Trial: spinning this spinner once. Event: the spinner landing on a prime number. Which group of outcomes should be written inside the box?
- 2, 3, 4, 5, 7
- 2, 3, 5, 7, 11
- 3, 5, 7, 11
- 4, 6, 9 ✓
- 2, 4, 6, 9
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- This incomplete outcome tree represents all outcomes from spinning spinner X twice and adding the results of each spin. In the sample space, match the letter to its value.
- a⇔6 ✓
- b⇔14 ✓
- c⇔15 ✓
- d⇔5 ✓
- e⇔10 ✓
- Trial: spinning this spinner once. Event 1: the spinner landing on a even number. Event 2: the spinner landing on a square number. Which of these outcomes should be written inside the box?
- 2
- 9
- 21 ✓
- 25
- 31 ✓
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Worksheet
Presentation
Lesson Details
Key learning points
- Possible outcomes for two events can be shown in an outcome tree diagram.
- The outcome tree diagram can be used to generate either an outcome table or list.
- An outcome tree can be generated from either an outcome table or list.
Common misconception
Every group of branches should have the same number of branches.
In a multi-staged trial, each stage may have a different number of outcomes. The number of branches in each group reflects the number of outcomes of a stage. This means each group of branches can be made from a different number of branches.
Keywords
Tree diagrams - Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.
Outcome tree - Each branch of an outcome tree shows a possible outcome from an event or from a stage of a trial. The full outcome tree shows all possible outcomes.
Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.