Chance a student drinks coffee or tea

Question

In a large class, 60\% of students drink coffee, 50\% drink tea, and 30\% drink both. What is the probability that a randomly chosen student drinks at least one of the two?

Accepted Answer

"At least one" means coffee or tea or both. If you simply add 60\% and 50\% you get 110\%, which is impossible. The reason is that everyone who drinks both was counted once inside the coffee group and again inside the tea group, so they were counted twice. Inclusion-exclusion repairs this by subtracting the overlap exactly once: P(	ext{coffee or tea}) = P(	ext{coffee}) + P(	ext{tea}) - P(	ext{both}). Plugging in the numbers, 0.60 + 0.50 - 0.30 = 0.80. So 80\% of students drink at least one drink. As a sanity check, split the class into four disjoint groups: only coffee 0.30, only tea 0.20…

Chance a student drinks coffee or tea

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