Calculating theoretical probabilities from probability trees (two events) | Maths

Starter quiz

What is the sum of the possible events A, B and C in this probability tree?

1 ✓

$/frac{7}{8}$

$/frac{1}{8}$

$/frac{2}{8}$
In a fair six-sided die, what is the probability of rolling a 2 and getting 'tails' in a single toss of a fair coin?

$\frac{1}{12}$ ✓

$\frac{1}{6}$

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

A and C have an equal chance of appearing in the trials. ✓

B is more likely to appear in the trials. ✓

B is less likely to appear in the trials than A.
What is the probability of this spinner landing on a vowel?

0.4 ✓

0.2

0.5

0.6
Alex believes that the likelihood of a spinner stopping on a shaded space is equal to an unshaded space. Is Alex correct?

Alex is correct. ✓

Alex is incorrect, it is less likely the spinner would land on a shaded space.

Alex is incorrect, it is more likely the spinner would land on a shaded space.
How many ways are there to get a sum of 7 when adding the results of two standard six-sided dice rolls?

5

6 ✓

7

Exit quiz

$If P(A) = <Math>\frac{1}{3}</Math> and P(A and D) = <Math>\frac{1}{5}</Math>, then what is P(D)?$

If P(A) = $\frac{1}{3}$ and P(A and D) = $\frac{1}{5}$ , then what is P(D)?

$\frac{3}{5}$ ✓

$\frac{1}{5}$

$\frac{2}{5}$
What is the error in this tree diagram?

Events B and F should sum to 1 but they don't.

Events A and C should sum to 1 but they don't.

Events D and E should sum to 1 but they don't.

Events E and F should sum to 1 but they don't. ✓
What is a suitable calculation for the probability of event B occurring, and event F not occurring?

$\frac{5}{6}*\frac{1}{4}$ ✓

$\frac{5}{6}+\frac{1}{4}$

$\frac{5}{6}*\frac{3}{4}$

$\frac{5}{6}+\frac{3}{4}$
If the first and second event in this tree diagram were both flipping a coin once, what would be the probability of event B and event F occurring?

$\frac{1}{4}$ ✓

$\frac{1}{2}$

$\frac{2}{6}$
What is the least likely (but not impossible) pair of events occurring in this tree diagram?

A then C ✓

A then D

B then E

B then F
Which pair of events has a more than even chance of occurring?

B and F ✓

B and E

A and C

A d D

Worksheet

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Lesson Details

Key learning points

The probability of an outcome can be found with a probability tree diagram showing all possible outcomes for two events.
The probability of a set of outcomes can be found using a probability tree diagram.
The probability of a set of outcomes can be found using a probability tree, even when outcomes are not equally likely.

Common misconception

When I see a probability tree, I always multiply the probabilities.

If a probability tree shows a two-stage trial, then the probability of an outcome is the product of the probabilities of the outcomes at each stage. The probability of an event is the sum of the probabilities of each outcome in the event.

Keywords

Outcome - An outcome is a result of a trial (e.g. getting heads when flipping a coin once or getting two heads when flipping a coin twice).
Event - An event is a subset of a sample space. i.e. An outcome or set of outcomes that may occur from a trial (e.g. flipping a coin twice and getting the same result each time).
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.
Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.