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Probability from a two-set Venn diagram

Probability from a two-set Venn diagram

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In a group of 40 people, 24 own a cat (\(C\)), 15 own a dog (\(D\)) and 7 own neither.

  1. Complete the Venn diagram to show the number of people in each region.
  2. One person is chosen at random. Find the probability that this person owns both a cat and a dog.
  3. Find the probability that a person chosen at random owns a dog but not a cat.
  4. Find the probability that a person chosen at random owns at least one of the two pets.

Solution:

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Answer:(a) cat only 18, both 6, dog only 9, neither 7 (b) \(\frac{3}{20}\) (c) \(\frac{9}{40}\) (d) \(\frac{33}{40}\)

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