Venn diagrams show how sets overlap and relate to each other. They are used to visualise and solve probability problems, especially in mutually exclusive events and conditional probability.
A Venn diagram is used to organise information into sets.
It shows which items belong to one group, another group, both groups, or neither group.
In GCSE Maths, you need to read values, place information in the correct regions, complete missing numbers, and use the diagram to find probabilities.
A group of items or values.
A diagram that shows sets using circles inside a rectangle.
The overlap where items belong to both sets.
Everything in one set or the other or both.
Items that do not belong to any of the sets shown.
The full set of all items being considered, shown by the rectangle.
The intersection contains items in both sets.
These contain items in one set only.
Items outside the circles still count in the universal set.
\( \frac{\text{number wanted}}{\text{total number}} \)
Belongs to both sets
Belongs to set A only
Belongs to set B only
Belongs to neither set
A Venn diagram sorts information into sets. The circles show sets, and the rectangle shows the universal set.
Items in both sets.
Items in A but not B.
Items in B but not A.
Items outside both circles.
If the question gives the number in both sets, put this in the overlap first.
Items in neither set go outside both circles but inside the rectangle.
Use the overlap.
Use one circle excluding the overlap.
Use everything in one circle or the other.
Use outside both circles.
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on reading Venn diagrams and finding probabilities.
The Venn diagram shows the numbers in the universal set.
Write down the numbers in set A.
Using the Venn diagram above, find the probability that a number chosen at random is in set B.
Using the Venn diagram above, find the probability that a number chosen at random is in both set A and set B.
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on completing Venn diagrams from given information.
There are 30 students in a class. 18 study French, 14 study German and 6 study both French and German.
Complete the Venn diagram.
Using the information above, find the probability that a student chosen at random studies French but not German.
Using the information above, find the probability that a student chosen at random studies neither French nor German.
Exam-style questions aligned with OCR GCSE Mathematics, emphasising set notation and probability from Venn diagrams.
The Venn diagram shows information about 40 people who were asked whether they like tea or coffee.
Find the probability that a person chosen at random likes tea.
Write down the value of \( n(Tea \cap Coffee) \).
Find \( P(Tea \cup Coffee) \).
A person is chosen at random from those who like coffee. Find the probability that this person also likes tea.
Put the overlap in first.
Use subtraction to find the single-set parts.
Include the outside region if needed.
For probability, use number wanted over total number.
Putting set totals straight into the circles without subtracting the intersection.
Forgetting the items in neither set.
Mixing up both, either, only and neither.
Using the wrong denominator in a probability calculation.
These are common mistakes students make when working with Venn diagrams in GCSE Maths.
A student places values in the intersection that do not belong to both sets.
The overlap (intersection) must only contain items that belong to both sets. Check conditions carefully.
A student double-counts values when working with totals.
When totals are given, subtract the overlap to avoid counting shared elements twice.
A student forgets that some values may be outside all sets.
Include the region outside the circles to represent values that are in neither set.
A student mixes up intersection and union.
“Both” means intersection (overlap). “Either” means union (everything in one or both sets).
A student uses a partial total instead of the full sample space.
Use the correct total based on the question. For overall probability, use the full number of items unless the sample space is restricted.
Practise solving problems using Venn diagrams.
Interpret Venn diagrams and calculate totals.
In a Venn diagram, 5 people are in set A only, 3 are in the overlap, and 7 are in set B only. How many are in set A?
In a Venn diagram, 6 are in A only and 4 are in the overlap. How many are in set A?
In a Venn diagram, 2 are in A only, 5 in overlap, 8 in B only. How many are in total (no outside)?
In a Venn diagram, 3 are in A only, 2 in overlap, 5 in B only, and 4 outside. Find the total.
What does the overlap in a Venn diagram represent?
In a Venn diagram, 7 are in B only and 3 in overlap. How many are in set B?
A student counts the overlap twice when finding the total. What is wrong?
In a Venn diagram, 4 are in A only, 6 in B only, 2 in overlap. How many are not in either set if total is 20?
Which region represents elements only in set A?
In a Venn diagram, 10 are in A only, 5 in overlap, 15 in B only. Find total in both sets.
Solve problems using set notation and probabilities from Venn diagrams.
In a group of 50 people, 20 like A, 30 like B, and 10 like both. How many like A or B?
In a group of 60 people, 25 like A, 20 like B, and 5 like both. Find how many like neither.
Which formula is correct?
In a group of 80 people, 40 like A, 30 like B, and 10 like both. Find how many like A only.
In a group of 100 people, 60 like A, 50 like B, and 20 like both. How many like neither?
In a group of 40 people, 18 like A, 22 like B, and 6 like both. Find n(A ∪ B).
A student adds A and B without subtracting overlap. What is wrong?
In a group of 70 people, 30 like A, 25 like B, and 5 like both. Find how many like neither.
Which represents A ∩ B?
In a group of 90 people, 45 like A, 35 like B, and 15 like both. Find how many like only B.
Practise this topic with interactive games.
Relationships between sets.
Items in both sets.
Items in either set.