M4.1 Probability and Venn diagrams - Probability and Venn diagrams

Oct 26, 2026

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M4.1 Probability and Venn diagrams teaches how to draw and interpret Venn diagrams and use set notation to model events. It explains standard probability symbols such as P(A), P(Ā), P(A∪B), and set intersection P(A∩B), then applies them to numbers represented in Venn diagrams. Worked examples show how to form fractions from set sizes or total counts, including complements and combined events. Exercises develop skills for multi-set probability problems.

LanguageEnglish

CategoryExam

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Before you start

Why do this?

Key Points

Practice Questions

Methods 4.1 Probability and Venn diagrams M4.1 Probability and Venn diagrams |
Before you start |
Why do this? | | | | | | --- | --- | --- | --- | --- | --- | | You should be able to:
draw and interpret Venn diagrams
ﬁnd the probability that an event will occur. | Venn diagrams can be used to help work out
probabilities. | | | | | |
Objective |
Get Ready | | | | | | You will be able to use set notation to describe | A bag contains 3 red, 2 blue and 6 green | | | | | | events. | counters. A counter is taken at random. What is | | | | | | You will be able to use Venn diagrams to ﬁnd | the probability that the counter is: | | | | | | probabilities. | 1 4 | red 2
blue or green | green | 3 5 | not green white | Key Points When working out probabilities from a Venn diagram: P(A) represents the probability that the item is in setA P(A 􀀙 ) represents the probability that the item is not in setA P(A 􀀙 ) 􀀕 1 􀀒 P(A) P(A 􀀞 B) represents the probability that the item is in both setA and set B P(A 􀀜 B) represents the probability that the item is in set A or in set B or in both sets. A number is taken at random from those shown on the Venn diagram. Find: a P(A) b P(A 􀀙 ) c P(A 􀀞 B) . a P(A) b P(A 􀀙 􀀕 __5 9 ) 􀀕 There are 9 numbers intotal inthe Venn diagram so 9 goes on the bo om of the fraction. There are 5 numbers altogether in set A so 5 goes on the top of the fraction. There are 4 numbers that are not in setA. Alternatively, work out 1 􀀒 c P(A 􀀞 B) 􀀕 A03 1 Chapter 4 Probability and Venn diagrams 1 The Venn diagram shows the whole numbers from 1 to 12. A number is chosen at random from those shown on the Venn diagram. Find: a P(B) b P(A 􀀞 B) c P(A 􀀜 B) 2 The Venn diagram shows the whole numbers from 1 to 10. A number is chosen at random from those shown on the Venn diagram. Find: a P(D) b P(D 􀀙 ) c P(C 􀀞 D) d P(C 􀀜 D) 3 a On a Venn diagram show: the whole numbers from 1 to 12 set E where E 􀀕 {2, 4, 6, 8, 10, 12} set F where F 􀀕 {1, 2, 3, 4, 6, 12} b A number is chosen at random from those in the Venn diagram. Find: i P(E) ii P(F􀀙 ) iii P(E 􀀞 F) iv P(E 􀀜 F) 4 a Draw a Venn diagram to show: 􀀅 􀀕 {integers from 10 to 20} E 􀀕 {even numbers} M 􀀕 {multiples of 5} b A number is chosen at random from those in the Venn diagram. Find: i P(M) ii P(E 􀀞 M) iii P(E 􀀜 M) iv P(E􀀙 􀀞 M) v P(E 􀀞 M) 􀀙 5 􀀅 􀀕 {integers from 1 to 20} M 􀀕 {multiples of 4} F 􀀕 {factors of 20} A number is chosen at random from the universal set, 􀀅 . Work out: a P(M) b P(F􀀙 ) c P(M 􀀞 F) d P(M 􀀜 F) e P(M􀀙 􀀞 F) 2 Methods 4.1 Probability and Venn diagrams The Venn diagram shows information about the students in Year 12. B 􀀕 {students who take Biology} C 􀀕 {students who take Chemistry} C B 49 17 7 44 If a student is chosen at random work out: a P(B) b P(B 􀀞 C ) c P(C 􀀞 B 􀀙 ) d P(B 􀀜 C) a P(B) 􀀕 _7 49 􀀑 44 􀀑 17 􀀑 7 􀀕 117 there are 117 students in Year 12, so the bo om number of each fraction will be 117. 44 􀀑 7 􀀕 51 so 51 students study Biology. b P(B 􀀞 C) 􀀕 _7 c P(C 􀀞 B 􀀙 ) 􀀕 d P(B 􀀜 C) 􀀕 7 is in the intersection. This shows that 7 students study Biology and Chemistry. 17 􀀑 7 􀀑 44 􀀕 68 so 68 students study Biology or Chemistry (or both). A03 Exercise 4B 1 Some students were asked if they played tennis or cricket. T C 3 7 2 8 The Venn diagram shows information about their answers. A student is chosen at random. Work out: a P(T) b P(C) c P(T 􀀞 C) 3 Chapter 4 Probability and Venn diagrams 2 In a group of 42 people, 13 belong to a badminton club, 19 belong to a tennis club and 7 belong to both a badminton and a tennis club. a Draw a Venn diagram to represent this information. A person is chosen at random from this group. b Find the probability that this person: i does not belong to a badminton club ii does not belong to either a badminton or a tennis club iii belon

FAQs

What does P(A) mean in probability with Venn diagrams?

P(A) represents the probability that the item is in set A, found by using the set’s count over the total shown on the diagram.

How is P(Ā) interpreted on a Venn diagram?

P(Ā) represents the probability that the item is not in set A, using the number of elements outside set A divided by the total.

What is the difference between P(A∪B) and P(A∩B) in these notes?

P(A∪B) is the probability of being in set A or set B (or both), while P(A∩B) is the probability of being in both sets at the same time.

Oct 26, 2026

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