Each branch of a probability tree shows a possible outcome from an event or from a stage of a trial, along with the probability of that outcome happening.

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

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

Comparing multiple representations to calculate theoretical probabilities for combined 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 Venn diagrams (two events)

Calculating theoretical probabilities from probability trees (two 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

What is the probability of event A and C happening?

An object chosen at random is most likely to be which of the following?

The event could be any of A, B, C, D, E or F

If one of the events below was much less likely to occur than any others, which statement would be true?

If each spinner is used once, what is the probability of the first spinner landing on 'A' and the second spinner not landing on '1'?

For a single event, what must all possibilities sum to? 

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

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 likelihood of A or C appearing in the first trial is the same.

The likelihood of A appearing in the second trial is high.

The likelihood of B appearing in both trials is more than equal chance.

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

In a fair six-sided die, what is the probability of rolling a 9 and getting 'tails' in a single toss of a fair coin?

A coin is flipped twice. Complete the sample space ξ = {HH, HT, {{}}, TT}

When rolling a fair six sided die, which event is more likely to occur?

Comparing multiple representations to calculate theoretical probabilities for combined events

Lesson outcome