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

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.

Event A is independent of event B if the probability of event A occurring is not affected by whether or not event B occurs.

Mutually exclusive events have no outcomes in common.

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

Comparing multiple representations to calculate conditional probabilities

Maths

Checking and securing displaying outcomes

Checking and securing exhaustive events

Probabilities involving algebra

Frequency trees

Checking and securing calculating probabilities from tables

Checking and securing calculating probabilities from diagrams

Experimental probability

Experimental vs theoretical probability

Set notation

Conditional probability in a two-way table

Conditional probability in a Venn diagram

Conditional probability in a tree diagram

Algebra in tree and Venn diagrams

Constructing three event Venn diagrams

Probabilities in three event Venn diagrams

Combinations

Advanced problem solving with conditional probability

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.

In this unit, pupils use their knowledge of calculating theoretical probabilities and extend it to calculate conditional probabilities.

Conditional probability

Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.

An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$a$$ = {{}}.

An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$d$$ = {{}}.

An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$x$$ is {{}}.

An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$w$$ is {{}}.

A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not.  P(RW') = {{}}. Give your answer as a decimal.

The probability of an outcome occurring given that another event has occurred is called {{}} probability. 

Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ⋃ M).

Sam asks 30 pupils if they take GCSE Art (A), GCSE Drama (D) or GCSE Music (M). The frequencies are shown in the Venn diagram. Find P(A ∩ M ∩ D').

Here is a frequency Venn diagram. P(A ⋃ B ⋃ C) = {{ }}. Give your answer as a decimal.

Here is a frequency Venn diagram. P(A ⋃ C′) = {{ }}. Give your answer as a decimal.

This frequency Venn diagram has 80 outcomes altogether. P(A ∩ B ∩ C) = $$\frac{1}{20}$$, P(A | B) = $$\frac{1}{3}$$ and P(A ⋃ B) = 0.7. $$y$$ = {{ }}.

Comparing multiple representations to calculate conditional probabilities

Lesson outcome