Probability

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

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

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

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.

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.