A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.

Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

An outcome table is a table that shows all the possible outcomes.

Problem solving with theoretical probability

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 Venn diagrams (two events)

Calculating theoretical probabilities from probability trees (two events)

Comparing multiple representations to calculate theoretical probabilities for combined events

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

Two dice are rolled and their values are added together. Assuming I drew the table as efficiently as I could, how many sides are on each dice?

The table shows the sample space for when two 8-sided dice are rolled and their values are added together. Which is the most likely outcome?

The table shows the sample space for when a 6-sided dice and a 4-sided dice are rolled and their values are added together. What is the probability that the dice sum to 5?

The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 9?

The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 7?

The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 6?

The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcome is most likely to happen?

The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcomes have a probability of $${3}\over{36}$$?

The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. What is the probability that the dice sum to 5?

Which calculation would increase 80 by 50%?

Problem solving with theoretical probability

Lesson outcome