They like tea, do they also like coffee?

Question

In a survey of 200 people, 120 said they like coffee and 80 said they do not. Among the 120 coffee lovers, 80 also like tea. Among the 80 who do not like coffee, 30 like tea. You pick one respondent at random and they turn out to like tea. What is the probability they also like coffee?

Accepted Answer

The clue "likes tea" restricts you to the tea lovers, so first count how many there are. - Coffee lovers who like tea: 80. - Non-coffee people who like tea: 30. Total tea lovers: 80 + 30 = 110. Of those, the ones who also like coffee number 80: P(	ext{coffee} \mid 	ext{tea}) = \frac{80}{110} = \frac{8}{11} \approx 0.727. You are not dividing by the whole survey of 200; conditioning on tea means the tea lovers become your new denominator. Takeaway. In a two-way table, a conditional probability is a row (or column) total in the denominator, not the grand total; pick the group the clue names f…

They like tea, do they also like coffee?

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