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Probability from a three-set Venn diagram

Probability from a three-set Venn diagram

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The Venn diagram shows how many of a group of 50 students study Art (\(A\)), Biology (\(B\)) and Chemistry (\(C\)). One student is chosen at random.

  1. Find \(\mathrm{P}(A\cap B)\).
  2. Find \(\mathrm{P}(A\cup C)\).
  3. Find the probability that the student studies exactly two of the subjects.
  4. Find \(\mathrm{P}\big((A\cup B)'\big)\).

Solution:

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Answer:(a) \(\frac{7}{50}\) (b) \(\frac{3}{5}\) (c) \(\frac{6}{25}\) (d) \(\frac{9}{25}\)

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