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Conditional probability from a three-set Venn diagram

Conditional probability from a three-set Venn diagram

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80 people were asked which of tea (\(T\)), coffee (\(C\)) and juice (\(J\)) they drink. The Venn diagram shows the results.

  1. A person who drinks tea is chosen at random. Find the probability that this person also drinks coffee.
  2. Given that a person chosen at random drinks exactly two of the drinks, find the probability that juice is one of the two drinks.
  3. Given that a person chosen at random does not drink coffee, find the probability that this person drinks juice.

Solution:

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Answer:(a) \(\frac{1}{3}\) (b) \(\frac{9}{16}\) (c) \(\frac{7}{27}\)

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