In a survey of 3125 people, 863 like tea and 2561 like coffee. The minimum number of people who like both tea and coffee, given that each of the surveyed people like at least one drink between tea and coffee, is:
299
Let T = people who like tea and C = people who like coffee. Since everyone likes at least one drink, \(n(T \cup C) = 3125\).
Using \(n(T \cup C) = n(T) + n(C) - n(T \cap C)\): \(3125 = 863 + 2561 - n(T \cap C)\).
So \(n(T \cap C) = 3424 - 3125 = 299\).
Because the union is fixed at the total surveyed, this value is forced, so the minimum number liking both drinks is 299.
Hence, the answer is 299.
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