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.

Calculating theoretical probabilities from lists (one event)

Maths

Checking listing possible outcomes

The probability scale

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)

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

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

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

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

A counter is picked at random from the bag. What is the probability that it contains the letter B?

A regular six-sided dice is rolled. What is the probability of rolling a 4?

A regular six-sided dice is rolled. Which event has a probability of $${4}\over{6}$$?

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

Which letter on the probability scale represents a probability of 0.5?

The spinner is divided into equal-sized sectors. What fraction of the spinner is labelled 'win'?

The spinner is divided into equal-sized sectors. {{}}% of the spinner is labelled 'lose'.

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 probability on an outcome is 25%. Approximately how many times could you expect the outcome to occur in 500 trials?

Calculating theoretical probabilities from lists (one event)

Lesson outcome