Probability

    OCR
    GCSE

    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.

    2
    Objectives
    3
    Exam Tips
    4
    Pitfalls
    7
    Key Terms
    4
    Mark Points

    Learning Objectives

    What you need to know and understand

    • Use tree diagrams to record probabilities of successive events.
    • Understand the concept of conditional probability and calculate it from first principles.

    Marking Points

    Key points examiners look for in your answers

    • Probabilities must be expressed as fractions, decimals, or percentages; ratios (e.g., 1:4) are generally not accepted for final answers.
    • Method marks (M) are awarded for showing the correct calculation path, such as multiplying probabilities along tree branches.
    • In 'Show that' questions, every step of the calculation must be written out explicitly; jumping to the answer loses credit.
    • For Venn diagrams, marks are awarded for placing elements in the correct regions, specifically handling the intersection correctly.

    Examiner Tips

    Expert advice for maximising your marks

    • 💡When asked for the probability of 'at least one', calculate 1 minus the probability of 'none' to save time and reduce error.
    • 💡Always check that the sum of probabilities on a set of tree diagram branches equals 1 before moving on.
    • 💡If the question involves 'frequency' or 'experimental data', use the term 'estimate' in your reasoning, as relative frequency is an estimate of probability.

    Common Mistakes

    Pitfalls to avoid in your exam answers

    • Writing probabilities as ratios (e.g., 3:4) instead of fractions (3/7), which results in zero marks for the final answer.
    • Failing to reduce the denominator in tree diagrams involving 'without replacement' scenarios.
    • Confusing the 'AND' rule (multiplication) with the 'OR' rule (addition) in complex multi-stage events.
    • Incorrectly identifying the region for 'A union B' in Venn diagrams by double-counting the intersection.

    Key Terminology

    Essential terms to know

    The Probability Scale and Notation
    Relative Frequency and Expectation
    Mutually Exclusive and Exhaustive Events
    Independent Events and the Multiplication Law
    Tree Diagrams and Frequency Trees
    Conditional Probability and Dependent Events
    Venn Diagrams and Set Notation

    Likely Command Words

    How questions on this topic are typically asked

    Calculate
    Complete
    Estimate
    Show that
    Work out
    Interpret

    Ready to test yourself?

    Practice questions tailored to this topic