In survey of 600 students in a school, 150 students were found to be taking tea &255 taking coffee,100 were taking both tea & coffee. Find how many students were taking neither tea nor coffee?
Answers
Answer:
- 325 students are taking neither tea nor coffee.
Step by step explanation
Given:
- Total students in the survey = 600
- Students who were taking tea = 150
- Students who were taking coffee = 225
- Students who were taking both tea and coffee = 100
To find:
- Students who were taking neither tea nor coffee
Solution:
Let's assume the set of students who are taking tea and coffee by T and C respectively. Also assume the students as the element of this set.
See the Venn Diagram in attachment.
We have to find the coloured region in Venn diagram.
Since,
the total number of students in the survey is 600, the universal set will have 600 elements
the total number of students who are taking tea is 150, the number of elements in set T will be 150 or n(T) = 150
the total number of students who are taking coffee is 225, the number of elements in set C will be 225 or n(C) = 225
the total number of students who are taking both tea and coffee is 100, the number of elements in set T intersection C will be 100 or n(T∩C) = 100
Now we have formula::
n(T∪C) = n(T) + n(U) - n(T∩C)
n(T∪C) = 150 + 225 - 100
n(T∪C) = 275
The value of union of set T and C is 275 it means that sum of all the students who are taking either tea and coffee is 275.
By subtracting this value from the universal set, we will obtain the value of students who were not taking either tea and coffee.
Students who are taking neither tea or coffee = 600 - 275
Students who are taking neither tea or coffee = 325
So 325 students are taking neither tea or coffee.
