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

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

A set of events are exhaustive if at least one of them has to occur whenever the experiment is carried out.

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

Checking and securing calculating probabilities from 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 set of events are {{}} if at least one of them has to occur whenever the experiment is carried out. 

A survey asked people whether they lived in Oakfield or not, and if they last shopped by online delivery or by going in-store. A random person is selected. Match each event to its probability.

A swimming club has 80 members. There are 13 members who swim both front crawl (FC) and butterfly (BF). The value of $$x$$ is {{}}.

This probability tree shows the probability of one of two events occurring.
The value of $$x$$ is {{}}.

Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. Use the probability tree to find the probability that they both lose their game.

Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. The probability that at least one of them loses their match is {{}}.

Students were asked whether they walked to school or used other transport methods, and how long their journey took them. Find the probability a student had a journey of 15 minutes or under.

A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(multiple of 5).

A spinner with outcomes {1, 2, 3, 5, 9, 15} is spun twice. The outcome of each spin is added together.
Find P(prime number).

People at a bus station were surveyed their age and where their destination was.
Match each frequency from the table to its value.

People at a bus station were surveyed their age and where their destination was.
A person is chosen at random. 
Find P(under 60 and going to Oakfield).

People at a bus station were surveyed their age and where their destination was.
A person going to Rowanwood is chosen at random. 
Find P(60 or over).

Starter Quiz