New

Calculating theoretical probabilities from probability tree diagrams (one event)

I can find theoretical probabilities from a probability tree diagram showing the possible outcomes for one event.

Download all

View unit

Lesson 5 of 13

New

Year 9

Calculating theoretical probabilities from probability tree diagrams (one event)

I can find theoretical probabilities from a probability tree diagram showing the possible outcomes for one event.

Download all

Lesson slides

Download lesson slides

Skip lesson slides

Lesson details

Key learning points

The probability of an outcome can be found by considering a probability tree diagram showing all possible outcomes.
The probability of a set of outcomes can be found by considering a probability tree showing all possible outcomes.
A probability tree can help us find a probability, even when the outcomes are not equally likely.

Keywords

Probability tree - 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.

Common misconception

A probability tree can only have two branches.

A probability tree can have any number of branches on a layer, but the more branches you want to include, the trickier and less practical the probability tree is to draw and use.

Probability trees can be used to show the probabilities of both individual outcomes and events from a trial.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Prior knowledge starter quiz

Download quiz pdf

6 Questions

Q1.
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?

Correct answer: $$\frac{1}{12}$$

$$\frac{1}{6}$$

$$\frac{1}{8}$$

Q2.
What is the probability that this spinner will land on R?

$$\frac{1}{8}$$

Correct answer: $$\frac{1}{5}$$

$$\frac{1}{3}$$

Q3.
A coin is flipped twice. Complete the sample space ξ = {HH, HT, , TT}

Correct answer: TH

Q4.
Andy tells his friend that this spinner is fair and that they have an equal chance of winning or losing. Is he right?

Andy is right

Correct answer: Andy is wrong

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

Q5.
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?

Correct answer: Sam is correct.

Sam is incorrect.

Q6.
When rolling a fair six sided die, which event is more likely to occur?

Rolling an even number

Rolling a prime number

Correct answer: Rolling a multiple of 1

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
What does a probability tree show?

Correct answer: All possible outcomes of an event and their probability

All possible outcomes of an event only

The most likely possible outcomes of an event only.

Q2.
Calculate the probability of event (A) in a probability tree if its branches have probabilities $$\frac{1}{4}$$, $$\frac{1}{3}$$, and (A)

Correct Answer: 5/12

Q3.
In a probability tree, each branch shows a possible outcome along with the of that outcome happening.

Correct answer: probability

risk

failure

guarantee

Q4.
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?

Correct Answer: 2/5, 0.4, 4/10

Q5.
If a two branched probability tree has a branch with probability $$\frac{1}{5}$$, what is the probability of the complementary event?

Correct Answer: 4/5, 0.8

Q6.
in a probability tree, branches coming from the same root should all sum to what?

Correct answer: 1

impossible to tell

0.5

Lesson appears in

UnitMaths / Probability: theoretical probabilities

Maths

Show unit

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Calculating theoretical probabilities from probability tree diagrams (one event)

Calculating theoretical probabilities from probability tree diagrams (one event)

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.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?

Q2.What is the probability that this spinner will land on R?

Q3.A coin is flipped twice. Complete the sample space ξ = {HH, HT, , TT}

Q4.Andy tells his friend that this spinner is fair and that they have an equal chance of winning or losing. Is he right?

Q5.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?

Q6.When rolling a fair six sided die, which event is more likely to occur?

Assessment exit quiz

6 Questions

Q1.What does a probability tree show?

Q2.Calculate the probability of event (A) in a probability tree if its branches have probabilities $$\frac{1}{4}$$, $$\frac{1}{3}$$, and (A)

Q3.In a probability tree, each branch shows a possible outcome along with the of that outcome happening.

Q4.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?

Q5.If a two branched probability tree has a branch with probability $$\frac{1}{5}$$, what is the probability of the complementary event?

Q6.in a probability tree, branches coming from the same root should all sum to what?

Lesson appears in

UnitMaths / Probability: theoretical probabilities

Maths

Q1.
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?

Q2.
What is the probability that this spinner will land on R?

Q3.
A coin is flipped twice. Complete the sample space ξ = {HH, HT, , TT}

Q4.
Andy tells his friend that this spinner is fair and that they have an equal chance of winning or losing. Is he right?

Q5.
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?

Q6.
When rolling a fair six sided die, which event is more likely to occur?

Q1.
What does a probability tree show?

Q2.
Calculate the probability of event (A) in a probability tree if its branches have probabilities $$\frac{1}{4}$$, $$\frac{1}{3}$$, and (A)

Q3.
In a probability tree, each branch shows a possible outcome along with the of that outcome happening.

Q4.
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?

Q5.
If a two branched probability tree has a branch with probability $$\frac{1}{5}$$, what is the probability of the complementary event?

Q6.
in a probability tree, branches coming from the same root should all sum to what?