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

Loading worksheet ...

Presentation

Loading presentation ...

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.