AQA · GCSE · Mathematics

    Course version: 8300 · Version from Sept 2015

    Relate relative expected frequencies to theoretical probability, using…

    Full specification wording

    Probability: relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale

    Relative expected frequency is the expected proportion of times an outcome occurs over many trials, expressed on the 0 to 1 scale.

    Checked against the AQA 8300 specification (opens in a new tab) on .

    • Point 3 of 10
    • 3 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    Relative expected frequency is the expected proportion of times an outcome occurs over many trials, expressed on the 0 to 1 scale. It is found by dividing the expected frequency count by the total number of trials, simplifying to the theoretical probability. For a fair six-sided die, the theoretical probability of rolling a 4 is 1/6. In 300 rolls, the expected frequency is 50, so the relative expected frequency is 50/300, which is 1/6. Theoretical probability assumes equally likely outcomes. Use precise language: 'expected frequency', 'theoretical probability', 'equally likely', and 'relative frequency'. Place probabilities on the 0 to 1 scale: 0 is impossible, 1 is certain, 0.5 is an even chance.

    What earns the marks

    • Defines relative expected frequency as a proportion on the 0 to 1 scale, equivalent to theoretical probability.
    • Distinguishes expected frequency (a count) from relative expected frequency (a proportion).
    • States theoretical probability as a fraction or decimal between 0 and 1 inclusive, or as a percentage between 0% and 100%.
    • Uses correct language such as 'expected frequency', 'theoretical probability', 'equally likely' and 'relative frequency'.
    • Places a given probability correctly on the 0 to 1 scale, recognising 0 as impossible and 1 as certain.

    Common mistakes and how to put them right

    • Confusing relative expected frequency with expected frequency.

      Put it right: The expected frequency is a count over trials, while relative expected frequency is a proportion from 0 to 1.

    • Writing a fractional or decimal probability greater than 1 or less than 0, for example 1.5 or -0.2.

      Put it right by checking the value lies within the 0 to 1 scale.

    • Treating a relative frequency from a small sample as proof that a die is biased.

      Put it right by explaining that random variation is larger in small samples.

    • Using vague language such as 'probably' without linking to the 0 to 1 scale.

      Put it right by stating the numerical probability and its position on the scale.

    Exam tips

    • Read the question carefully to decide whether it asks for a probability/proportion (0 to 1) or an expected frequency (a count).
    • When calculating relative expected frequency, show it as a fraction of the total trials, which simplifies to the theoretical probability.
    • When comparing data with theory, refer to the number of trials and whether the observed relative frequency is close to the theoretical probability.

    Try the lesson

    The start of the Probability: relate relative expected frequencies to theoretical probability, using appropriate language and the 0 to 1 probability scale lesson, made from checked teaching notes for this specification point.

    Have a go first

    A fair six-sided dice is rolled 60 times. How many times would you expect it to land on a 4?

    Listen

    Relative expected frequency is the expected proportion of times an outcome occurs over many trials, expressed on the 0 to 1 scale. It is found by dividing the expected frequency count by the total number of trials, simplifying to the theoretical probability. For a fair six-sided die, the theoretical probability of rolling a 4 is 1/6. In 300 rolls, the expected frequency is 50, so the relative expected frequency is 50/300, which is 1/6. Theoretical probability assumes equally likely outcomes. Use precise language: 'expected frequency', 'theoretical probability', 'equally likely', and 'relative frequency'. Place probabilities on the 0 to 1 scale: 0 is impossible, 1 is certain, 0.5 is an even chance. A strong answer earns marks for these points. Defines relative expected frequency as a proportion on the 0 to 1 scale, equivalent to theoretical probability. Distinguishes expected frequency (a count) from relative expected frequency (a proportion). States theoretical probability as a fraction or decimal between 0 and 1 inclusive, or as a percentage between 0% and 100%. Uses correct language such as 'expected frequency', 'theoretical probability', 'equally likely' and 'relative frequency'. A common slip: Writing a fractional or decimal probability greater than 1 or less than 0, for example 1.5 or -0.2. Instead, checking the value lies within the 0 to 1 scale. Exam tip: Read the question carefully to decide whether it asks for a probability/proportion (0 to 1) or an expected frequency (a count).

    See it

    A top-down flowchart with ten nodes. The first node states that theoretical probability assumes equally likely outcomes, and an arrow leads to the theoretical probability of rolling a 4 being 1/6. An arrow leads to the expected frequency of 50 in 300 rolls, then to the relative expected frequency of 50/300, then to 50/300 simplifying to 1/6, then to the relative expected frequency equalling the theoretical probability. An arrow leads to placing probabilities on the 0 to 1 scale, which branches into three nodes: 0 is impossible, 0.5 is an even chance, and 1 is certain.
    It shows how the expected frequency of 50 in 300 rolls gives a relative expected frequency of 50/300, which simplifies to the theoretical probability 1/6, and how probabilities sit on the 0 to 1 scale.

    Key words

    Say what each word means before you turn the card.

    Relative expected frequency

    Try answering aloud or in your head before turning the card.

    Theoretical probability

    Try answering aloud or in your head before turning the card.

    The 0 to 1 probability scale

    Try answering aloud or in your head before turning the card.

    See every definition
    Relative expected frequency
    The expected proportion of times an outcome occurs over many trials, expressed on the 0 to 1 scale, found by dividing the expected frequency count by the total number of trials.
    Theoretical probability
    A probability that assumes equally likely outcomes, stated as a fraction or decimal between 0 and 1 inclusive, or as a percentage between 0% and 100%.
    The 0 to 1 probability scale
    A scale on which 0 is impossible, 1 is certain and 0.5 is an even chance.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart with ten nodes. The first node states that theoretical probability assumes equally likely outcomes, and an arrow leads to the theoretical probability of rolling a 4 being 1/6. An arrow leads to the expected frequency of 50 in 300 rolls, then to the relative expected frequency of 50/300, then to 50/300 simplifying to 1/6, then to the relative expected frequency equalling the theoretical probability. An arrow leads to placing probabilities on the 0 to 1 scale, which branches into three nodes: 0 is impossible, 0.5 is an even chance, and 1 is certain.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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