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

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

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

Calculating theoretical probabilities from a table (one event)

Maths

Checking listing possible outcomes

The probability scale

Calculating theoretical probabilities from lists (one event)

Calculating theoretical probabilities from probability tree diagrams (one event)

Calculating theoretical probabilities from Venn diagrams (one event)

Comparing multiple representations to calculate theoretical probabilities

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

The table shows data about the number of animals in a zoo. An animal is selected at random. Which animal has a probability of $${5}\over{26}$$ of being chosen?

A group of people were surveyed and asked which of the three places they last visited. A participant in the survey is then chosen at random. What is the probability that they responded 'museum'?

The tally chart shows the number of cars in a car park of each colour. A car is chosen at random from the car park. What is the probability that it is blue?

The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is odd?

The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is prime?

The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is an odd prime?

The table shows data about the number of animals in a zoo. How many animals are there in total?

What is the probability that this spinner lands on 'B'?

What is the probability that this spinner lands on 'A'?

A regular six sided dice is rolled. What is the probability of rolling a 5?

Starter Quiz

Which numbers are not prime?