# Probability

Scheme of work: GCSE Foundation: Year 9: Term 5: Probability

#### Prerequisite Knowledge

• Compare and order fractions whose denominators are all multiples of the same number
• identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• add and subtract fractions with the same denominator and denominators that are multiples of the same number

#### Success Criteria

• Record, describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
• apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
• Relate relative expected frequencies to theoretical probability, using appropriate language and the 0 – 1 probability scale
• 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
• calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

#### Key Concepts

• Use the probability scale and associated keywords to compare the likelihood of the occurrence of an event.
• When writing probabilities as a fraction using the probability scale to show equivalences with the keywords
• Discuss the effect of bias and sample size when comparing theoretical and experimental probabilities.
• Use the random function on a calculator or spreadsheet to demonstrate simple randomisation.
• When listing the outcomes of combined events ensure students use a logical and systematic method.
• Branches on a probability tree have a sum of one as they are mutually exclusive.

#### Common Misconceptions

• Writing probabilities as a ratio is a common misconception.
• When creating Venn diagrams students often forget to place the remaining events outside the circles.
• When listing permutations of combined events students often repeat events when they do not use a logical and systematic method.

## Probability Resources

### Mr Mathematics Blog

#### Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

#### GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

#### Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.