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      Using a Venn diagram to display outcomes for two events

      Lesson details

      Learning outcome

      I can systematically find all the possible outcomes for two events by using a Venn diagram.

      Key learning points

      1. Possible outcomes for two events can be shown in a Venn diagram.
      2. The Venn diagram can be used to generate any of the other models.
      3. Any of the other outcome diagrams can be used to generate a Venn diagram.

      Keywords

      • Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

      Common misconception

      Pupils may not draw the rectangle in their Venn diagrams.

      Refer back to the rectangle hosting all possible outcomes; the sample space and therefore a vital part of a Venn diagram.

      Teacher tip

      Although Venn diagrams are typically drawn using circles, rectangles can be used for ease on squared paper/workbooks.

      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.
      Select the prime number.

      6
      Correct answer: 7
      8
      9
      10

      Q2.
      Which of these statements are true about square numbers?

      Correct answer: Square numbers are never prime.
      Square numbers can be non-integer.
      Correct answer: Square numbers have an odd number of distinct factors.
      Every square's area is a square number.

      Q3.
      Here are all the factors of a number $$x$$. Match each factor with the factor that completes the factor pair.

      Correct Answer:1,24

      24

      Correct Answer:2,12

      12

      Correct Answer:3,8

      8

      Correct Answer:4,6

      6

      Q4.
      Which of these numbers is 48 a multiple of?

      Correct answer: 3
      5
      7
      Correct answer: 8
      11

      Q5.
      The sample space is the set of all possible from a trial.

      Correct Answer: outcomes

      Q6.
      Which outcome is not a factor of 6 but is even?

      An image in a quiz
      1
      2
      3
      Correct answer: 4
      5

      6 Questions

      Q1.
      Which of these is a Venn diagram?

      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q2.
      Use this Venn diagram to match the events to the outcomes.

      An image in a quiz
      Correct Answer:event A,{12, 14, 15, 20, 31, 72}

      {12, 14, 15, 20, 31, 72}

      Correct Answer:event B,{10, 15, 20, 59, 99}

      {10, 15, 20, 59, 99}

      Correct Answer:not event A,{10, 18, 44, 59, 62, 99}

      {10, 18, 44, 59, 62, 99}

      Correct Answer:not event B,{12, 14, 18, 31, 44, 62, 72}

      {12, 14, 18, 31, 44, 62, 72}

      Correct Answer:event A and event B,{15, 20}

      {15, 20}

      Correct Answer:event A or event B,{10, 12, 14, 15, 20, 31, 59, 72, 99}

      {10, 12, 14, 15, 20, 31, 59, 72, 99}

      Q3.
      The Venn diagram shows 5 pupils and whether they play football (F) or play rugby (R). Which pupil plays rugby but not football?

      An image in a quiz
      Jun
      Alex
      Sofia
      Correct answer: Izzy
      Jacob

      Q4.
      This Venn diagram shows prime numbers (P) and odd numbers (O). The Venn diagram has two errors. What are they?

      An image in a quiz
      The outcomes are not in numerical order.
      Correct answer: The outcomes of the sample space are not all represented.
      The circles are not labelled A and B.
      Correct answer: There is a duplication of an outcome.

      Q5.
      There are outcomes in the sample space shown in this Venn diagram.

      An image in a quiz
      Correct Answer: 6, six

      Q6.
      Which Venn diagram shows the same information as this outcome tree?

      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz

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