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.

Calculating theoretical probabilities from probability tree 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 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

All possible outcomes of an event and their probability

The most likely possible outcomes of an event only.

Calculate the probability of event (A) in a probability tree if its branches have probabilities $$\frac{1}{4}$$, $$\frac{1}{3}$$, and (A)

In a probability tree, each branch shows a possible outcome along with the {{}} of that outcome happening.

If a probability tree has three branches with two branches having probabilities $$\frac{1}{5}$$ and $$\frac{2}{5}$$, what is the probability of the third outcome?

If a two branched probability tree has a branch with probability $$\frac{1}{5}$$, what is the probability of the complementary event?

in a probability tree, branches coming from the same root should all sum to what?

In a fair six-sided die, what is the probability of rolling a 3 and getting a head in a single toss of a fair coin?

What is the probability that this spinner will land on R?

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

There is no way of telling if the spinner is fair.

Andy tells his friend that this spinner is fair and that they have an equal chance of winning or losing. Is he right?

Sam thinks that if you place six consecutive whole numbers on each segment of this spinner, you will always have an equal chance of spinning an odd or an even number. Is Sam correct?

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

Starter Quiz

In a fair six-sided die, what is the probability of rolling a 3 and getting a head in a single toss of a fair coin?