AI generatedProbabilityKey Stage 3

Finding a missing frequency in a Venn diagram

Finding a missing frequency in a Venn diagram.

  • The rectangle is the universal set. The overlap belongs to both sets.
  • Fill the overlap first; subtract it from each set total to find the “only” regions.
  • Union means either or both; intersection means both; complement means outside the named set.

Example 1

There are 14 people in total. 6 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?25?
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 4; neither = 3.
Two-set Venn diagramξAB4253

Example 2

There are 17 people in total. 8 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?35?
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 5; neither = 4.
Two-set Venn diagramξAB5354

Your turn

Question 1

There are 20 people in total. 10 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?45?
Check answer
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 6; neither = 5.
Two-set Venn diagramξAB6455
Question 2

There are 23 people in total. 12 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?55?
Check answer
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 7; neither = 6.
Two-set Venn diagramξAB7556
Question 3

There are 26 people in total. 14 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?65?
Check answer
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 8; neither = 7.
Two-set Venn diagramξAB8657
Question 4

There are 29 people in total. 16 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?75?
Check answer
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 9; neither = 8.
Two-set Venn diagramξAB9758
Question 5

There are 27 people in total. 12 belong to A, including those in both sets. Complete the missing frequencies.

Two-set Venn diagramξAB?26?
Check answer
The total for A includes the overlap.
NeitherSubtract every region inside the circles once.
A only = 10; neither = 9.
Two-set Venn diagramξAB10269
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