Venn-diagram probability
Edexcel GCSE Maths revision on Venn-diagram probability. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
In a group of 20 students, 12 study French and 8 study German. If 3 students study both languages, how many students study only French?
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Answer: 9
To find the number of students who study only French, you subtract the 3 students who study both languages from the 12 total French students, which gives 9. A common mistake is to ignore the overlap and simply count all French students without removing the duplicates.
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Question 2
Which set notation represents the region where two sets A and B overlap in a Venn diagram?
- A) A intersection B
- B) A union of the B
- C) A complement of B
- D) A minus the set B
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Answer: A intersection B
The correct answer is A intersection B, represented by the symbol that looks like an arch. Many students confuse this with A union B, which represents the entire area covered by both sets combined.
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Question 3
A class of 30 pupils are asked if they own a cat or a dog. 15 own a cat, 12 own a dog, and 5 own neither. How many pupils own both a cat and a dog?
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Answer: 2
Since 5 pupils own neither, 25 pupils must own at least one pet. Adding the cat owners (15) and dog owners (12) gives 27, which exceeds 25 by 2, meaning these 2 pupils must have been counted twice because they own both.
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.