Answer: The percentage of students signed up for neither canoeing nor trekking m=32%
Step-by-step explanation:
Given: The total number of students in summer camp n(S)=120
Number of students signed up for canoeing n(C)=72
Number of students signed up for trekking m(T)= 23
Number students signed up for trekking and canoeing n(C∩T)=13
Number of students signed up for only canoeing (Not trekking)=\(72-13=59\)
Number of students signed up for only trekking (Not canoeing)=\(23-13=10\)
Now, the number of students signed up for either trekking or canoeing is given by :-
\(n(C\cup T)=n(S)+n(C)-n(C\cap T)\\\\\Rightarrow n(C\cup T)=72+23-13=82\)
Number of students signed up for neither trekking nor canoeing is given by :-\((n(C\cup T))'=n(S)-n(C\cup T)=120-82=38\)
The percentage of students signed up for neither canoeing nor trekking
\(=\frac{38}{120}\times100=31.6666666667\approx32\%\)
