GCSE Maths Practice: venn-diagrams

Question 6 of 10

GCSE Maths (Higher): Find the probability that a student likes exactly one of Science or Maths.

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\( \begin{array}{l}\textbf{In a school of 800 students, 500 like Science,}\\\textbf{400 like Maths, and 300 like both subjects.}\\\textbf{What is the probability that a randomly chosen student}\\\textbf{likes exactly one of Science or Maths?}\end{array} \)

Diagram

Choose one option:

For “exactly one”, subtract the overlap from each group, then add the two “only” results.

GCSE Maths (Higher): “Exactly one” with Venn Diagrams

This question is more challenging than a standard “or” probability because it asks for exactly one subject.

Key idea

Exactly one means:

  • Science only
  • Maths only

It does not include students who like both subjects.

Step-by-step

  1. Find Science only: subtract those who like both
    \(500 - 300 = 200\)
  2. Find Maths only: subtract those who like both
    \(400 - 300 = 100\)
  3. Add the two “only” parts
    \(200 + 100 = 300\)
  4. Divide by the total
    \(\frac{300}{800}\)

Common mistakes

  • Using \(500+400-300\) (that finds or, not exactly one).
  • Including the overlap (students who like both) even though “exactly one” excludes them.

Exam tip

If you see exactly one, think: (A only) + (B only).

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