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.

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

Calculating theoretical probabilities from Venn diagrams (two events)

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)

Comparing multiple representations to calculate theoretical probabilities

Summing probabilities

Calculating theoretical probabilities from two-way tables (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

Using this Venn diagram, what is the probability of an object being randomly selected from B?

Using this Venn diagram, what is the probability of an object being randomly selected that is in A and B?

Using the diagram, what is P(A and not B)?

Using the diagram, what is P(not A and not B)?

B is the most likely letter to appear in the trials.

C is the least likely letter to appear in the trials.

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

If the probability of an event (A) is $$/frac{2}{5}$$, and the experiment is repeated 25 times, what is the theoretical number of times event (A) will occur?

The letter selected would most likely be a vowel

The letter selected would most likely be a consonant

The letter selected would most likely be an 'S'

The letter selected would least likely be an 'M'

A random character is selected from the word MISSISSIPPI, which of the following statements are true? 

If the probability of an event (A) is $$/frac{1}{8}$$, and the experiment is repeated 40 times, what is the theoretical number of times event (A) will occur?

If you roll a fair six sided die twice and sum the results, what is the most likely sum below? 

Calculating theoretical probabilities from Venn diagrams (two events)

Lesson outcome