Probability

    AQA
    A-Level

    Probability is the mathematical study of uncertainty, quantifying the likelihood of events occurring on a scale from 0 (impossible) to 1 (certain). It encompasses both theoretical probability, based on equally likely outcomes, and experimental probability, derived from relative frequency and large data sets. Mastery of this topic requires the ability to model single and combined events using sample spaces, Venn diagrams, and tree diagrams to calculate probabilities for independent, mutually exclusive, and conditional scenarios.

    0
    Objectives
    3
    Exam Tips
    3
    Pitfalls
    7
    Key Terms
    4
    Mark Points

    What You Need to Demonstrate

    Key skills and knowledge for this topic

    • Award M1 for correct identification of the conditional group in the denominator when calculating P(A|B)
    • Award A1 for the correct application of the addition rule P(A U B) = P(A) + P(B) - P(A n B)
    • Credit responses that explicitly demonstrate the test for independence: showing P(A n B) = P(A) x P(B)
    • Award B1 for a fully correct Venn diagram with all probabilities summing to 1, including the region outside the sets

    Example Examiner Feedback

    Real feedback patterns examiners use when marking

    • "You have correctly calculated the intersection, but you must explicitly state the comparison to P(A)xP(B) to prove independence"
    • "Check your denominator for the conditional probability part — remember it is 'given that', so the sample space shrinks"
    • "Your Venn diagram is missing the probability outside the circles; ensure the total sums to 1"
    • "Excellent use of set notation; to secure full marks, ensure you define your events clearly at the start"

    Marking Points

    Key points examiners look for in your answers

    • Award M1 for correct identification of the conditional group in the denominator when calculating P(A|B)
    • Award A1 for the correct application of the addition rule P(A U B) = P(A) + P(B) - P(A n B)
    • Credit responses that explicitly demonstrate the test for independence: showing P(A n B) = P(A) x P(B)
    • Award B1 for a fully correct Venn diagram with all probabilities summing to 1, including the region outside the sets

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When asked to 'Show that' events are independent, you must calculate P(A) x P(B) and P(A n B) separately and explicitly state they are equal
    • 💡Use Venn diagrams for questions involving 'at least one' or 'neither' to visually verify which regions to sum
    • 💡Pay close attention to the phrase 'given that'; this signals conditional probability and dictates the denominator

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Assuming events are independent without evidence, rather than testing for independence using P(A n B) = P(A) x P(B)
    • Confusing mutually exclusive events (intersection is zero) with independent events (intersection is product of probabilities)
    • In conditional probability questions, failing to adjust the denominator to reflect the restricted sample space

    Key Terminology

    Essential terms to know

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Determine
    Explain
    Show that
    Interpret
    State

    Practical Links

    Related required practicals

    • •{"code":"LDS","title":"AQA Large Data Set","relevance":"Probabilities may be calculated from frequency tables derived from the LDS (e.g., car data)"}

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