Probability

Scheme of work: Year 12 A-Level: Applied: Statistics: Probability

Prerequisite Knowledge

• Apply ideas of randomness, fairness and equally likely events to calculate the expected outcomes of multiple future experiments
• Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
• Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
• Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
• Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

Success Criteria

• Understand the meanings of terms used in probability;
• Calculate probabilities of single events;
• Identify and use sample spaces
• Draw and interpret Venn diagrams;
• Understand mutually exclusive and independent events and determine whether two events are independent
• Use and understand tree diagrams

Key Concepts

• Students may need a recap of interpolation when finding a probability from grouped data;
• Link probability to interpreting histograms and interpolation.
• Whilst Venn diagrams are covered at GCSE it may be necessary to recap identifying regions using set notation.
• Students should be able to describe the terms mutually exclusive and independent using Venn diagrams.
• While it is not required at AS it is useful to introduce the Addition Rule when discussing the union of two sets and P(A) â¨‰ P(B) = P(AnB) for independent events.
• In addition to visualising that mutually exclusive sub-sets have no overlap students should understand P(A) n P(B) = 0 and P(A) + P(B) = P(AuB) for mutually exclusive events.

Common Misconceptions

• Some students confuse the terms mutually exclusive and independent, especially when using their formulae.
• When drawing Venn diagrams some students forget to include the box for the universal set.
• More complicated, wordy problems can often be simplified by sketching either a Venn diagram or probability tree.

Probability Resources

Mr Mathematics Blog

Estimating Solutions by Rounding to a Significant Figure

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Transforming Graphs Using Function Notation

Guide for teaching how to transform graphs using function notation for A-Level mathematics.