Probability, Outcomes and Venn Diagrams

Students learn how to use two-way tables, sample space and Venn Diagrams to calculate the probability of two or more events happening.  As learning progresses they use set notation to describe whether events are mutually exclusive.

This unit takes place in Year 8 Term 6 and follows on from Chance and Probability.

Probability, Outcomes and Venn Diagrams Lessons
4 Part Lesson
Calculating a Probability from Sample Space Diagrams
4 Part Lesson
Probabilities That Add Up to One
4 Part Lesson
Understanding Set Notation
4 Part Lesson
Calculating Probabilities from Two-Way Tables
4 Part Lesson
Venn Diagrams
Additional Resources
Extended Learning
Two-way tables
Extended Learning
Mutually Exclusive Events
Extended Learning
Venn Diagrams
Venn Diagrams and Set Notation
Expectation and Mutually Exclusive Events
Prerequisite Knowledge
  • Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale.
Key Concepts
  • A sample space diagram is used to show all the outcomes from a combination of two events.  This follows on from Permutations of Two Events.
  • Mutually exclusive outcomes are those that cannot occur together.  For example, when you toss a coin you can not get a head and a tails.
  • A set is a collection of items or numbers.  Sets are shown by curly brackets { }.  The items or numbers in a set are called elements.
  • Venn diagrams are used to display sets and show where they overlap.  Circles are used to represent each set.  The rectangle that contains the sets is called the universal set.  Elements that belong to more than one set are shown through the overlap between the set’s circles.
Working mathematically

Develop fluency

  • Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

  • Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
Subject Content


  • Understand that the probabilities of all possible outcomes sum to 1
  • Enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams
  • Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

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