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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.

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New
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 resources
Share activities with pupils

Lesson details

Key learning points

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

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.

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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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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?
An image in a quiz
$$\frac{1}{8}$$
Correct answer: $$\frac{1}{5}$$
$$\frac{1}{3}$$
Q3.
A coin is flipped twice. Complete the sample space ξ = {HH, HT, , TT}
HH
HT
Correct answer: TH
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?
An image in a quiz
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?
An image in a quiz
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

Exit quiz

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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