Comparing multiple representations to calculate theoretical probabilities | Maths

Starter quiz

In a fair six-sided die, what is the probability of rolling a 6 and getting a head in a single toss of a fair coin?

$\frac{1}{6}$

$\frac{1}{12}$ ✓

$\frac{1}{2}$
What is the probability that this spinner will land on an odd number?

1

$\frac{1}{3}$

$\frac{2}{3}$ ✓
What is the probability that the letter B is selected at random from this bag?

$\frac{3}{8}$ ✓

$\frac{5}{8}$

$\frac{3}{4}$
A coin is flipped three times. Which outcome is missing from the following sample space? ξ = {HHH, HHT, HTH, HTT, ______, THT, TTH, TTT}

THH ✓

TTH

TTT

THT
What is the probability of the spinner landing on either A or B?

$/frac{1}{3}$ ✓

$/frac{1}{2}$

$/frac{1}{4}$

Exit quiz

If Set A = {𝜸, 𝜹} and Set B = {𝞵,𝜹, 𝜽}, what symbol is missing from the Venn diagram?

𝞵 ✓

𝜹

𝜷
Which of the following represents set B?

{ } (empty)

{◖, ▶, □ } ✓

{◖, ▶, □, ■ }
Which of the following represents set A?

{ } (empty)

{◖, ▶, □ }

{◖, ▶, □, ■ } ✓

{ ■ }
If set A = {2,4,7} and set B = {5}, what is the error in the diagram?

There should be no '4' in the left circle.

The '5' should be in the intersection.

The '7' should be in A, but not in the intersection. ✓
Which of the following is a correct statement about this diagram

There is nothing in Set B that is not in Set A ✓

Set B is empty

Set A contains 1 object

There is nothing in Set A that is not in Set B
Use the Venn diagram to write the probability P(only A)

$\frac{3}{4}$

$0$

$\frac{1}{4}$ ✓

$\frac{1}{2}$

Worksheet

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Lesson Details

Key learning points

The probability of an outcome can be calculated from each representation.
Different representations show the same information in different ways.
Some representations may be easier to use than others, depending on the context.

Common misconception

Venn diagrams are useful when generating a complete list of outcomes and showing the probabilities of that list.

Venn diagrams can be very useful when categorising already known outcomes into events. The Venn diagram can then be used to calculate probabilities. However, Venn diagrams are not as useful when generating a list of outcomes.

Keywords

Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property.
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.
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Theoretical probability - Theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.
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.