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      Equally likely outcomes

      Lesson details

      Learning outcome

      I can state when outcomes will be equally likely.

      Key learning points

      1. A set of possible outcomes can be stated.
      2. Outcomes can be evaluated to decide how likely they are.
      3. Outcomes with the same likelihood can be identified.

      Keywords

      • Outcome - An outcome is a result of a trial.

      • Likelihood - Likelihood describes the chance that a particular event will occur.

      • Trial - A trial is a single predefined test.

      • 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.

      Common misconception

      Rolling a 6 on a dice is less likely to happen than rolling other numbers. Or ticket 001 is less likely to be drawn in a raffle than other tickets.

      The random nature of picking a raffle or rolling a dice means all outcomes are equally likely as each other.

      Teacher tip

      Ask pupils to design a their own single-trial game where the likelihoods of winning and losing are equal.

      Licence

      This content is © Oak National Academy Limited (2026), 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 all the numbers that are multiples of 3.

      0.3
      1
      Correct answer: 3
      Correct answer: 6
      Correct answer: 9

      Q2.
      Select all the numbers that are factors of 3.

      0.3
      Correct answer: 1
      Correct answer: 3
      6
      9

      Q3.
      What fraction of the circle is shaded?

      An image in a quiz
      $${1}\over{3}$$
      $${3}\over{7}$$
      Correct answer: $${3}\over{10}$$
      $${3}\over{13}$$

      Q4.
      In which diagrams is half of the circle shaded?

      An image in a quiz
      Correct Answer: 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

      Q5.
      Jun wants to shade in $${1}\over{3}$$ of this whole circle. Jun should shade in sectors of the circle.

      An image in a quiz
      Correct Answer: 4, four, four sectors, 4 sectors

      Q6.
      Match each letter to the fraction of the circle that is labelled with that letter.

      An image in a quiz
      Correct Answer:a,$${1}\over{4}$$

      $${1}\over{4}$$

      Correct Answer:b,$${1}\over{3}$$

      $${1}\over{3}$$

      Correct Answer:c,$${5}\over{12}$$

      $${5}\over{12}$$

      6 Questions

      Q1.
      Match each key words with its definition.

      Correct Answer:trial,a single predefined test

      a single predefined test

      Correct Answer:outcome,a result of a trial

      a result of a trial

      Correct Answer:sample space,all the possible outcomes of a trial

      all the possible outcomes of a trial

      Correct Answer:likelihood,describes the chance that a particular event will occur

      describes the chance that a particular event will occur

      Q2.
      Complete the following sample space for the outcomes of the spinner. ξ = {A, I, L, R, }.

      An image in a quiz
      Correct Answer: T

      Q3.
      In which spinners are the outcomes 'win' and 'lose' equally likely?

      An image in a quiz
      Correct Answer: 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

      Q4.
      Which outcomes are equally likely in this spinner?

      An image in a quiz
      Correct answer: A and B
      A and C
      B and C

      Q5.
      In which spinners are all the outcomes equally likely?

      Correct Answer: An image in a quiz
      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

      Q6.
      A regular six-sided dice is rolled once. In which sample space are the outcomes equally likely?

      ξ = {factor of 6, not a factor of 6}
      ξ = {multiple of 3, not a multiple of 3}
      Correct answer: ξ = {odd, even}
      ξ = {square number, not a square number}

      To help you plan your 9 maths lesson on: Equally likely outcomes, download all teaching resources for free and adapt to suit your pupils' needs...