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.

Algebra in tree and 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

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 total frequency is {{ }}.

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

A pack of cards contains 30 “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 cats).

Two events A and B are mutually exclusive. This means that....

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school. Match each value to its probability.

Sofia has to catch a bus and then a train to get to school. When the bus is late, Sofia is more likely to miss the train and so be late for school.  P(Sofia is late for school) = {{ }}.

Here is a general probability tree. Which of these probabilities give the probability of the highlighted events? 

One marble is taken at random from a bag of 7 purple and 5 green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows these two events. Find the value of $$z$$.

One marble is taken at random from a bag of purple and green marbles. The marble is not replaced. A second marble is then taken. The tree diagram shows the two events. Find P(at least 1 green marble).

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

Algebra in tree and Venn diagrams

Lesson outcome

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