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

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 Venn diagrams (one event)

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)

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

Which of the following is the correct data set for A?

When throwing a fair sided die, what is the probability of not getting a 6? 

What is the intersection of the sets A {𝜷, 𝜸, 𝜹} and B {𝜷, 𝜽}

Which of the following is the correct data set for B?

When throwing a fair sided die, what is the probability of not getting a multiple of 3? 

What is the correct set of outcomes, ξ , shown in this Venn diagram?

What is the probability that this spinner will land on either L or T?

A coin is flipped twice. How many possible outcomes will be in the sample space?

If the probability of an event (A) is 1/6, and the experiment is repeated 78 times, what is the theoretical number of times (A) will occur?

In a bag with 5 red counters and 3 green counters, what is the probability of randomly selecting a red counter?

In a bag with 5 red counters, 2 blue counters and 3 green counters, what is the probability of randomly selecting a blue counter?

In a fair six-sided die, what is the probability (as a decimal) of rolling an even number and getting a head in a single toss of a fair coin?

Calculating theoretical probabilities from Venn diagrams (one event)

Lesson outcome