Maths · Topic 1: Year 10
Probability
Combined events and sample spaces, mutually exclusive events, experimental probability, independent events and tree diagrams, conditional probability, and Venn diagrams with set notation.
Lessons
Ticks are remembered on this device only.
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1
Combined events
List the outcomes of two events systematically, use sample space diagrams, and work out probabilities of combined events.
6 terms -
2
Mutually exclusive events
Use the addition rule for mutually exclusive events, find the probability of an event not happening, and complete probability tables.
6 terms -
3
Experimental probability
Estimate probabilities from experiments using relative frequency, predict how many times an event will happen, and judge whether a coin or dice is fair.
6 terms -
4
Independent events and tree diagrams
Recognise independent events, multiply probabilities along the branches of a tree diagram, and add the probabilities of the outcomes you want.
6 terms -
5
Conditional probability
Work out probabilities when one event changes the next, such as taking items without replacement, and use two-way tables to find conditional probabilities.
6 terms -
6
Venn diagrams and set notation
Use set notation, draw and complete Venn diagrams, and use them to find probabilities, including conditional probabilities at Higher tier.
6 terms
Downloads
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- Combined events.pptx Built from the lesson script on 30 September 2026. View
- Combined events - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Combined events - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Mutually exclusive events.pptx Built from the lesson script on 30 September 2026. View
- Mutually exclusive events - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Mutually exclusive events - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Experimental probability.pptx Built from the lesson script on 30 September 2026. View
- Experimental probability - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Experimental probability - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Independent events and tree diagrams.pptx Built from the lesson script on 30 September 2026. View
- Independent events and tree diagrams - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Independent events and tree diagrams - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Conditional probability.pptx Built from the lesson script on 30 September 2026. View
- Conditional probability - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Conditional probability - Exam Questions.docx Built from the lesson script on 30 September 2026. View
- Venn diagrams and set notation.pptx Built from the lesson script on 30 September 2026. View
- Venn diagrams and set notation - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Venn diagrams and set notation - Exam Questions.docx Built from the lesson script on 30 September 2026. View
Key terms in this chapter
All 36, gathered from every lesson.
- Outcome
- One possible result of an event.
- Event
- One or more outcomes.
- Equally likely
- Each outcome has the same chance.
- Sample space
- The set of all possible outcomes.
- Sample space diagram
- A table or list showing every outcome.
- Probability
- A number from 0 to 1 showing how likely an event is.
- Mutually exclusive
- Events that cannot happen at the same time.
- Probability scale
- A line from 0 (impossible) to 1 (certain).
- Complement
- The event "not A", with probability \(1 - P(A)\).
- Exhaustive
- A set of events that covers every possible outcome.
- Biased
- Not fair; outcomes are not equally likely.
- Random
- Every item has the same chance of being chosen.
- Trial
- One repeat of an experiment.
- Frequency
- How many times an outcome happens.
- Relative frequency
- Frequency divided by the number of trials.
- Theoretical probability
- The probability worked out from equally likely outcomes.
- Expected number
- Probability multiplied by the number of trials.
- Fair
- Every outcome is equally likely.
- Independent
- The outcome of one event does not change the other.
- Tree diagram
- A diagram showing the outcomes of events and their probabilities on branches.
- Branch
- A line on a tree diagram carrying a probability.
- With replacement
- Putting the item back before the next pick.
- Combined event
- Two or more events considered together.
- Complement
- The event "not A".
- Conditional probability
- The probability of an event given that another has happened.
- Without replacement
- The item is not put back, so later probabilities change.
- Dependent events
- Events where one affects the probability of the other.
- Tree diagram
- A diagram showing outcomes and probabilities on branches.
- Two-way table
- A table showing two categories at once.
- Complement
- The event "not A".
- Set
- A collection of items.
- Element
- One item in a set.
- Universal set
- The set of everything being considered, \(\xi\).
- Union
- Items in one set or the other or both, \(\cup\).
- Intersection
- Items in both sets, \(\cap\).
- Complement
- Items not in the set, \(A'\).