Calculating theoretical probabilities from Venn diagrams (two events) | Maths

Starter quiz

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

The most likely outcome is {B,B}.

B is the most likely letter to appear in the trials. ✓

C is the least likely letter to appear in the trials.
If the probability of an event (A) is $/frac{2}{5}$ , and the experiment is repeated 25 times, what is the theoretical number of times event (A) will occur?

5

10 ✓

15

20

25
A random character is selected from the word MISSISSIPPI, which of the following statements are true?

The letter selected would most likely be a vowel

The letter selected would most likely be a consonant ✓

The letter selected would most likely be an 'S'

The letter selected would least likely be an 'M' ✓
If the probability of an event (A) is $/frac{1}{8}$ , and the experiment is repeated 40 times, what is the theoretical number of times event (A) will occur?

1

8

5 ✓

18
If you roll a fair six sided die twice and sum the results, what is the most likely sum below?

7 ✓

6

8
If you roll a fair six sided die twice and sum the results, what is the most likely sum below?

an even sum

an odd sum

An even or an odd sum are equally likely ✓

Exit quiz

Using this Venn diagram, what is the probability of an object being randomly selected from B?

$\frac{5}{7}$ ✓

$\frac{2}{7}$

$\frac{2}{5}$

$\frac{5}{6}$
Using this Venn diagram, what is the probability of an object being randomly selected that is in A and B?

$\frac{5}{7}$

$\frac{3}{7}$ ✓

$\frac{1}{2}$

$\frac{6}{7}$
Using the diagram, what is P(A and not B)?

$\frac{5}{7}$

$\frac{3}{7}$

$\frac{1}{7}$ ✓

$\frac{4}{7}$
Using the diagram, what is P(not A and not B)?

$\frac{5}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

$\frac{1}{7}$ ✓
Using the diagram, what is P(not A and not B)?

$\frac{2}{7}$ ✓

$\frac{3}{7}$

$\frac{4}{7}$

$\frac{1}{7}$
Using the diagram, what is P(A and B)?

$\frac{2}{7}$

$\frac{3}{7}$

$\frac{4}{7}$

$\frac{1}{7}$ ✓

Worksheet

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Lesson Details

Key learning points

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

Common misconception

Pupils may struggle with finding the probability of A or B, and may count the outcomes that belong to A and B twice.

If you use an example, such as visiting particular countries, ask the pupils how someone would respond to the question 'have you visited X or Y' if they have in fact visited both countries.

Keywords

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.
Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.