In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?
AnswerLet T and C is the set of students who take tea and coffee respectively.
n(T) = 150, n(C) = 225, n(T ∩ C) = 100
Use formula
n ( T ∪ C ) = n ( T ) + n ( C ) – n ( T ∩ C)
Plug the values we get,
= [150 + 225 - 100]
⇒ 275
Students taking neither tea nor coffee
⇒ Total students - student taking tea or coffee
⇒600 – 275
⇒ 325
Hence, 325 students were taking neither tea nor coffee.
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