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

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.

Theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.

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.

Comparing multiple representations to calculate theoretical probabilities

Maths

Checking listing possible outcomes

The probability scale

Calculating theoretical probabilities from lists (one event)

Calculating theoretical probabilities from a table (one event)

Calculating theoretical probabilities from probability tree diagrams (one event)

Calculating theoretical probabilities from Venn diagrams (one event)

Summing probabilities

Calculating theoretical probabilities from two-way tables (two events)

Calculating theoretical probabilities from Venn diagrams (two events)

Calculating theoretical probabilities from probability trees (two events)

Comparing multiple representations to calculate theoretical probabilities for combined events

Problem solving with theoretical probability

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. 

In this unit we build upon the concept of likelihood to work more mathematically with more measurable probability using fraction and decimal representations to both interpret and calculate. We revisit and develop ways to represent and compare probabilities.

Probability: theoretical probabilities

If Set A = {𝜸, 𝜹} and Set B = {𝞵,𝜹, 𝜽}, what symbol is missing from the Venn diagram?

There should be no '4' in the left circle.

The '7' should be in A, but not in the intersection.

If set A = {2,4,7} and set B = {5}, what is the error in the diagram?

There is nothing in Set B that is not in Set A

There is nothing in Set A that is not in Set B

Which of the following is a correct statement about this diagram

Use the Venn diagram to write the probability P(only A)

In a fair six-sided die, what is the probability of rolling a 6 and getting a head in a single toss of a fair coin?

What is the probability that this spinner will land on an odd number?

What is the probability that the letter B is selected at random from this bag?

A coin is flipped three times. Which outcome is missing from the following sample space? ξ = {HHH, HHT, HTH, HTT, {{}}, THT, TTH, TTT}

What is the probability of the spinner landing on either A or B?

Starter Quiz

In a fair six-sided die, what is the probability of rolling a 6 and getting a head in a single toss of a fair coin?