Chance and Probability

Introducing Probability with Fractions

Comparing the Probability of Events

Permutations of Two Events

Estimate Probabilities from Experimental Data

Predicting Outcomes using Probability

Prerequisite Knowledge

• Compare and order fractions, including fractions > 1
• Use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Key Concepts

• The terms outcome, event and probability are key to describing the likelihood of an event occurring
  • Outcome is the result of an experiment
  • An event is a set of outcomes of a probability experiment
  • Probability describes the likelihood of an event occurring.  A probability can be given as fraction, decimal or percentage.
• An event which is impossible has a  probability of zero.  An event which is certain to occur has a probability of one.
• When listing all the permutations of two or more events students need a logical and exhaustive systematic method.
• When working with experimental data a probability can only be estimated as contextual factors are likely to have been a factor in the outcome.

Working mathematically

Develop fluency

• Use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Reason mathematically

• Explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Solve problems

• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
• Begin to model situations mathematically and express the results using a range of formal mathematical representations

Subject Content

Probability

• Record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale.
• Understand that the probabilities of all possible outcomes sum to 1
• Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.