What fraction of the office likes tea or coffee?

Question

An office of 50 people is surveyed: 30 like tea, 25 like coffee, and 10 like both. Pick one person at random. What is the probability they like tea or coffee (at least one)?

Accepted Answer

You cannot just add 30 and 25: the 10 people who like both are in each count, so they would be counted twice. Inclusion-exclusion on the counts gives the number who like at least one drink: T \cup C = T + C - T \cap C = 30 + 25 - 10 = 45. So 45 of the 50 people like at least one, and P(T \cup C) = \frac{45}{50} = 0.90. As a check, the four disjoint groups are: tea only 30 - 10 = 20, coffee only 25 - 10 = 15, both 10, and neither 50 - 45 = 5. They sum to 50. Takeaway. A \cup B = A + B - A \cap B is inclusion-exclusion for counts, the same rule as for probabilities. Subtracting the "both" group…

What fraction of the office likes tea or coffee?

Your answer

More Probability questions