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Venn diagrams practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of Venn diagrams questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

Only A = 4, both = 4, only B = 4, neither = 4. Find P(A or B).

Show answer

Answer: 3/4

  1. Inside circles: 4 + 4 + 4 = 12. Total: 16.
  2. Fraction: 12/16 = 3/4.
  • Method (1): Inside circles: 4 + 4 + 4 = 12. Total: 16.
  • Accuracy (1): Fraction: 12/16 = 3/4.

Question 2 Easy

Only A = 1, both = 3, only B = 2, neither = 4. Find P(A or B).

Show answer

Answer: 3/5

  1. Inside circles: 1 + 3 + 2 = 6. Total: 10.
  2. Fraction: 6/10 = 3/5.
  • Method (1): Inside circles: 1 + 3 + 2 = 6. Total: 10.
  • Accuracy (1): Fraction: 6/10 = 3/5.

Question 3 Medium

Only A = 2, both = 1, only B = 3, neither = 4. What is the probability of neither?

Show answer

Answer: 2/5

  1. Neither: 4. Total: 10.
  2. Fraction: 4/10 = 2/5.
  • Method (1): Neither: 4. Total: 10.
  • Accuracy (1): Fraction: 4/10 = 2/5.

Question 4 Medium

Only A = 5, both = 2, only B = 3, neither = 10. What is the probability of neither?

Show answer

Answer: 1/2

  1. Neither: 10. Total: 20.
  2. Fraction: 10/20 = 1/2.
  • Method (1): Neither: 10. Total: 20.
  • Accuracy (1): Fraction: 10/20 = 1/2.

Question 5 Hard

Only A = 1, both = 3, only B = 2, neither = 4. What is the probability of A?

Show answer

Answer: 2/5

  1. Set A: 1 + 3 = 4. Total: 10.
  2. Fraction: 4/10 = 2/5.
  • Method (1): Set A: 1 + 3 = 4. Total: 10.
  • Accuracy (1): Fraction: 4/10 = 2/5.

Question 6 Hard

Only A = 8, both = 2, only B = 5, neither = 5. What is the probability of A?

Show answer

Answer: 1/2

  1. Set A: 8 + 2 = 10. Total: 20.
  2. Fraction: 10/20 = 1/2.
  • Method (1): Set A: 8 + 2 = 10. Total: 20.
  • Accuracy (1): Fraction: 10/20 = 1/2.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

Only A = 6, both = 2, only B = 4, neither = 8. What is the probability of neither?

Show answer

Answer: 2/5

  1. Total is 6 + 2 + 4 + 8 = 20.
  2. Neither region is 8.
  3. Probability is 8 / 20 = 2/5.
  • Method (1): Calculate total: 6 + 2 + 4 + 8 = 20
  • Method (1): Form fraction 8/20 using the neither region 8
  • Accuracy (1): 2/5

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

In a Venn diagram, what does "A or B" include?

  1. Only A, only B, and the overlap (both)
  2. Only the overlap
  3. Only A and only B
Show answer

Only A, only B, and the overlap (both) Union A ∪ B includes everything inside either circle.

Check 2

In a Venn diagram, what does "A and B" represent?

  1. Only the central overlap
  2. All items in either circle
  3. Items outside both circles
Show answer

Only the central overlap Intersection A ∩ B is the shared lens.

Check 3

What does "neither A nor B" represent?

  1. The region outside both circles
  2. The overlap
  3. Only set A
Show answer

The region outside both circles Items that belong to neither category lie in the surrounding box.

Check 4

only A = 2, both = 1, only B = 3, neither = 4. What is the total count?

  1. 10
  2. 6
  3. 9
Show answer

10 2 + 1 + 3 + 4 = 10.

Check 5

only A = 2, both = 1, only B = 3, neither = 4. What is P(A or B)?

  1. 3/5
  2. 1/2
  3. 1/10
Show answer

3/5 (2 + 1 + 3) / 10 = 6/10 = 3/5.

Check 6

only A = 2, both = 1, only B = 3, neither = 4. What is P(A and B)?

  1. 1/10
  2. 3/10
  3. 3/5
Show answer

1/10 Overlap is 1 out of total 10.

Check 7

only A = 2, both = 1, only B = 3, neither = 4. What is P(neither)?

  1. 2/5
  2. 3/5
  3. 1/10
Show answer

2/5 4 / 10 = 2/5.

Check 8

only A = 2, both = 1, only B = 3, neither = 4. What is P(A)?

  1. 3/10
  2. 1/5
  3. 6/10
Show answer

3/10 Circle A includes only A + both = 2 + 1 = 3 out of 10.

Check 9

only A = 5, both = 2, only B = 3, neither = 10. What is P(A or B)?

  1. 1/2
  2. 7/20
  3. 3/10
Show answer

1/2 (5 + 2 + 3) / 20 = 10/20 = 1/2.

Check 10

only A = 5, both = 2, only B = 3, neither = 10. What is P(neither)?

  1. 1/2
  2. 1/4
  3. 3/10
Show answer

1/2 10 / 20 = 1/2.

Check 11

only A = 1, both = 3, only B = 2, neither = 4. What is P(A and B)?

  1. 3/10
  2. 3/5
  3. 1/10
Show answer

3/10 3 out of 10.

Check 12

only A = 1, both = 3, only B = 2, neither = 4. What is P(A)?

  1. 2/5
  2. 1/10
  3. 3/10
Show answer

2/5 (1 + 3) / 10 = 4/10 = 2/5.

Check 13

Why does P(A) include the overlap?

  1. Every element in the overlap belongs to A (as well as B)
  2. It is an arbitrary convention
  3. Because A is always drawn on the left
Show answer

Every element in the overlap belongs to A (as well as B) The circle for set A encloses both the unique region and the intersection.

Check 14

only A = 4, both = 4, only B = 4, neither = 4. What is P(A or B)?

  1. 3/4
  2. 1/2
  3. 1/4
Show answer

3/4 (4 + 4 + 4) / 16 = 12/16 = 3/4.

Check 15

only A = 3, both = 3, only B = 6, neither = 3. What is P(neither)?

  1. 1/5
  2. 1/4
  3. 1/3
Show answer

1/5 3 / 15 = 1/5.

Keep going with Venn diagrams

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