Calculating theoretical probabilities from probability tree diagrams (one event) | Maths

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?

$\frac{1}{12}$ ✓

$\frac{1}{6}$

$\frac{1}{8}$
What is the probability that this spinner will land on R?

$\frac{1}{8}$

$\frac{1}{5}$ ✓

$\frac{1}{3}$
A coin is flipped twice. Complete the sample space ξ = {HH, HT, ______, TT}

HH

HT

TH ✓

TT
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

Andy is wrong ✓

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

Sam is correct. ✓

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

Rolling an even number

Rolling a prime number

Rolling a multiple of 1 ✓

Exit quiz

What does a probability tree show?

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

'5/12' ✓
In a probability tree, each branch shows a possible outcome along with the ______ of that outcome happening.

probability ✓

risk

failure

guarantee
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?

'2/5' ✓
If a two branched probability tree has a branch with probability $\frac{1}{5}$ , what is the probability of the complementary event?

'4/5' ✓
in a probability tree, branches coming from the same root should all sum to what?

1 ✓

impossible to tell

0.5

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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.

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.