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).

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

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).

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

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

Constructing three event Venn diagrams

Maths

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

Conditional probability

A __________ space is all the possible outcomes of a trial.

Izzy asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. {{}} pupils take music but not drama.

Izzy asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. {{}} pupils do not take drama.

{prime numbers} is a subset of {odd numbers}

{prime numbers} and {odd numbers} are mutually exclusive

{prime numbers} and {multiples of 4} are mutually exclusive

A spinner is numbered with the integers from 80 to 89. The incomplete outcome Venn diagram is used to display 3 events. Select the correct statements. 

What region is shown shaded in this Venn diagram?

This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. Which of these probability statements are correct?

This probability Venn diagram shows the probability of a random spinner (spun once) landing on a square number or a factor of 36. The value of $$x$$ is {{}}. Give your answer as a decimal.

Here is a frequency Venn diagram. P(A ∩ B) = 0.2. The value of $$x$$ is {{ }}.

P(C given D) = 0.4. Which of these equations is correct to find the value of $$x$$?

A pack of cards contains 50 “character” (c) cards and some “spell” (s) cards. A card is taken at random, replaced and a 2nd card is taken. P(two spell cards) = 0.25. There are {{ }} cards in the deck.

The ratio of cats (c) to dogs (d) in an animal shelter is 4 : 3. Two random animals are taken from the shelter for adoption. Find an expression for P(2 dogs).

This lesson will be removed by end of Summer Term 2025.

Constructing three event Venn diagrams

Lesson outcome

This lesson will be removed by end of Summer Term 2025.