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Chapter Overview
Learning Goals
Learning Goals
Maths
Summary
A set is a collection of 'things' known as elements. In statistics, sets are usually presented on a Venn diagram. This provides an easy way for the probability of an element, inside a given set, to be worked out.
Sets are represented by a list of elements inside two curly brackets: { }
The set of even numbers between 1 and 10:
On a Venn diagram, each set is represented by a circle which contains all the elements within it.
Set Notation | Definition | Venn diagram Representation |
n(A) | Number of elements in set A. | |
The empty set ∅ | A set which has nothing in it. | |
Universal Set ξ or E or U | The set containing all elements. | ![]() |
Complement A′ or A | All elements not in A. | ![]() |
Intersection A∩B | All elements in both A and B. | ![]() |
Union A∪B | All elements in either A or B or both. | ![]() |
Conditional (A given B) A∣B | All elements in A given they are in B. | ![]() |
Disjoint sets | Two sets that share none of the same elements. | ![]() |
Subset A⊂B | A is a set inside of B. | ![]() |
You can use Venn diagrams to work out the probability of an event by counting the number of elements in the relevant set and taking that as a fraction out of the total.
The Venn diagram shows the numbers of students that said they liked green and blue.
Find the probability that when selected at random, a pupil would like:
1. The colour green:
N(Year 11 Students)=100
Work out the number of students that like green.
n(G)=20+23=43
Work out the probability that a student likes green.
P(G)=10043
2. Both blue and green:
Work out the number of students that like both blue and green.
n(B∩G)=20
Work out the probability that a student likes both blue and green.
P(B∩G)=10020=51
3. Blue given they like green:
Take the number of students that like both blue and green as a fraction out of the number that like green.
n(G)=43 n(B∩G)=20P(B∣G)=4320
Note: In the example above 25 is the number of students that did not fit into either category - they did not like blue or green!
A set is a collection of 'things' known as elements. In statistics, sets are usually presented on a Venn diagram. This provides an easy way for the probability of an element, inside a given set, to be worked out.
Sets are represented by a list of elements inside two curly brackets: { }
The set of even numbers between 1 and 10:
On a Venn diagram, each set is represented by a circle which contains all the elements within it.
Set Notation | Definition | Venn diagram Representation |
n(A) | Number of elements in set A. | |
The empty set ∅ | A set which has nothing in it. | |
Universal Set ξ or E or U | The set containing all elements. | ![]() |
Complement A′ or A | All elements not in A. | ![]() |
Intersection A∩B | All elements in both A and B. | ![]() |
Union A∪B | All elements in either A or B or both. | ![]() |
Conditional (A given B) A∣B | All elements in A given they are in B. | ![]() |
Disjoint sets | Two sets that share none of the same elements. | ![]() |
Subset A⊂B | A is a set inside of B. | ![]() |
You can use Venn diagrams to work out the probability of an event by counting the number of elements in the relevant set and taking that as a fraction out of the total.
The Venn diagram shows the numbers of students that said they liked green and blue.
Find the probability that when selected at random, a pupil would like:
1. The colour green:
N(Year 11 Students)=100
Work out the number of students that like green.