Answer: Â Option 'A' is correct.
Step-by-step explanation:
Since we have given that
Total number of students at a summer camp (Universal set)= 150
Number of students who signed for canoeing (C) = 72
Number of students who signed for trekking (T)=23
Number of student who signed for both (T∩C)= 13
As we know the formula of "Sets ":
[tex]n(T\cup C)=n(T)+n(C)-c(T\cap C)\\\\n(T\cup C)=72+23-13\\\\n(T\cup C)=82[/tex]
So, we need to find the number of students who signed up for neither canoeing nor trekking:
[tex]n(T\cup C)'=n(U)-n(T\cup C)\\\\n(T\cup C)'=150-82\\\\n(T\cup C)'=68[/tex]
Percentage of students signed up for neither canoeing nor trekking is given by
[tex]\frac{68}{150}\times 100\\\\=45.33\4\\\\=45\%[/tex]
Hence, Option 'A' is correct.
