When listing outcomes systematically, they are listed in such a way as to ensure all outcomes are recorded.

Checking listing possible outcomes

Maths

In the future unit, pupils use their knowledge of calculating theoretical probabilities and extend this understanding to calculating conditional probabilities using all of the representations encountered in this unit.

In the prior unit, pupils learnt techniques for systematically listing all of the possible outcomes for both one event and two events. In this unit, pupils use lists of outcomes to find theoretical probabilities. 

In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.

Probability: theoretical probabilities

The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

The probability scale

A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

Calculating theoretical probabilities from lists (one event)

The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property.

Calculating theoretical probabilities from a table (one event)

Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

Calculating theoretical probabilities from probability tree diagrams (one event)

Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Calculating theoretical probabilities from Venn diagrams (one event)

A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.

Theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

Comparing multiple representations to calculate theoretical probabilities

Two events are mutually exclusive if they share no common outcome.

Summing probabilities

Calculating theoretical probabilities from two-way tables (two events)

Calculating theoretical probabilities from Venn diagrams (two events)

An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice).

An event is a subset of a sample space. i.e. An outcome or set of outcomes that may occur from a trial (e.g. flipping a coin twice and getting the same result each time).

Calculating theoretical probabilities from probability trees (two events)

Comparing multiple representations to calculate theoretical probabilities for combined events

Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

An outcome table is a table that shows all the possible outcomes.

Probability: theoretical probabilities

Choose a lesson (13)

These lessons will be removed by end of Summer Term 2025.