# 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

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing