Venn-diagram probability
AQA GCSE Maths revision on Venn-diagram probability. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
A Venn diagram shows two overlapping sets, A and B. What does the region outside both circles represent?
- A) The union of A and B
- B) The intersection of A and B
- C) The complement of the union of A and B
- D) The universal set
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Answer: The complement of the union of A and B
The union of A and B represents everything inside either circle. Anything outside these circles is therefore not part of A or B, which is mathematically defined as the complement of the union.
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Question 2
If event A and event B are mutually exclusive, what must be true about their Venn diagram representation?
- A) The circles must overlap
- B) The circles must not touch
- C) The intersection region must be empty
- D) The universal set must be empty
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Answer: The intersection region must be empty
Mutually exclusive means the probability of both occurring is zero. In a Venn diagram, this is visualised by having no overlap between the two sets.
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Question 3
A student claims that for any two sets A and B, P(A or B) = P(A) + P(B). Under what specific condition is this student's claim correct?
- A) When A and B are independent
- B) When A and B are mutually exclusive
- C) When A is a subset of B
- D) When the universal set is empty
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Answer: When A and B are mutually exclusive
The general addition rule is P(A or B) = P(A) + P(B) - P(A and B). If the events are mutually exclusive, P(A and B) is zero, leaving only the sum of the individual probabilities.
Want to test yourself on the remaining cards for this topic?
13 more questions on Venn-diagram probability — plus mistakes tracking and spaced repetition across the whole Maths spec.