Question

. In a survey of 300 students in a school, 75 students are found to be drinking tea
and 125 students are found to be drinking coffee, 50 were drinking both tea and
coffee. Find how many students drink neither tea nor coffee.​

Answer 1

Answer:

Let U be the set of all students who took part in the survey.

Let T be the set of students taking tea.

Let C be the set of students taking coffee.

n(U)=600,n(T)=150,n(C)=225,n(T∩C)=100

To find: Number of student taking neither tea nor coffee i.e., we have to find n(T

′

∩C

′

).

n(T

′

∩C

′

)=n(T∪C)

′

=n(U)−n(T∪C)

=n(U)−[n(T)+n(C)−n(T∩C)]

=600−[150+225−100]

=600−275

=325

Hence, 325 students were taking neither tea nor coffee.