Calculating theoretical probabilities from Venn diagrams (one event) | Maths

Starter quiz

What is the probability that this spinner will land on either L or T?

0.4 ✓

0.2

0.6
A coin is flipped twice. How many possible outcomes will be in the sample space?

2

4 ✓

3
If the probability of an event (A) is 1/6, and the experiment is repeated 78 times, what is the theoretical number of times (A) will occur?

13 ✓

6

36

18
In a bag with 5 red counters and 3 green counters, what is the probability of randomly selecting a red counter?

$/frac{5}{3}$

$/frac{5}{8}$ ✓

$/frac{2}{5}$
In a bag with 5 red counters, 2 blue counters and 3 green counters, what is the probability of randomly selecting a blue counter?

$/frac{1}{5}$ ✓

$/frac{2}{9}$

$/frac{7}{10}$
In a fair six-sided die, what is the probability (as a decimal) of rolling an even number and getting a head in a single toss of a fair coin?

'0.25' ✓

Which of the following is the correct data set for A?

{2, 4, 7} ✓

{2, 4}

{7}

{2,4,5,7}
When throwing a fair sided die, what is the probability of not getting a 6?

$\frac{1}{6}$

$\frac{6}{6}$

$\frac{5}{6}$ ✓
What is the intersection of the sets A {𝜷, 𝜸, 𝜹} and B {𝜷, 𝜽}

{𝜷} ✓

{𝜷, 𝜸, 𝜹, 𝜽}

{𝜷, 𝜷, 𝜸, 𝜹, 𝜽}
Which of the following is the correct data set for B?

{4,2}

{4,2,7}

{7}

{5}

{5,7} ✓
When throwing a fair sided die, what is the probability of not getting a multiple of 3?

$\frac{1}{3}$ ✓

$\frac{1}{6}$

$\frac{1}{4}$

$\frac{5}{6}$
What is the correct set of outcomes, ξ , shown in this Venn diagram?

ξ = {2,4,5,7} ✓

ξ = {2,4,7}

ξ = {7}

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

Pupils may count the number of outcomes and state this as the probability.

Remind pupils that the probability scale is between 0 and 1, so an answer of 3 is not correct.

Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.
Theoretical probability - A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.