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.

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

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

Comparing multiple representations to calculate theoretical probabilities for combined events

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. 

Probability: theoretical probabilities

What is the probability of event A and C happening? 

An object chosen at random is most likely to be which of the following? 

The event could be any of A, B, C, D, E or F

If one of the events below was much less likely to occur than any others, which statement would be true? 

If each spinner is used once, what is the probability of the first spinner landing on 'A' and the second spinner not landing on '1'? 

For a single event, what must all possibilities sum to? 

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

A trial has three possible outcomes: {A, B, C}. P(A) = $${2}\over{7}$$. P(B) = $${1}\over{7}$$. P(C) = $${4}\over{7}$$. Which outcome is most likely to happen?

The likelihood of A or C appearing in the first trial is the same.

The likelihood of A appearing in the second trial is high.

The likelihood of B appearing in both trials is more than equal chance.

There are two trials. In Trial 1, a spinner with {A, B, C} is spun twice. In Trial 2, a spinner with {B, C} is spun twice. Which statement is true?

In a fair six-sided die, what is the probability of rolling a 9 and getting 'tails' in a single toss of a fair coin?

A coin is flipped twice. Complete the sample space ξ = {HH, HT, {{}}, TT}

When rolling a fair six sided die, which event is more likely to occur?

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

Comparing multiple representations to calculate theoretical probabilities for combined events

Lesson outcome

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