Question

Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.
Use a two-way table to organize the information and answer the following question:

Approximately what percentage of students signed up for neither canoeing nor trekking?

72%
40%
54%
98%

Answer 1

That is 72%of the kids

Answer 2

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

Total number of students = 180

Number of students who signed for canoeing (C) = 72

Number of students who signed for trekking (T) = 23

Number of student who signed for trekking is also signed for canoeing = 13

Number of students who only signed for canoeing (C) = 72-13=59

Number of students who only signed for trekking (T) = 23-13=10

So, Number of students who signed up either for canoeing or trekking is given by

$n(C\cup T)=n(C)+n(T)-n(C\cap T)\\\\n(C\cup T)=72+23-13\\\\n(C\cup T)=95-13\\\\n(C\cup T)=82$

So, Number of students who signed up neither for canoeing not trekking is given by

$n(C\cup T)'=n(U)-n(C\cup T)\\\\n(C\cup T)'=180-82\\\\n(C\cup T)'=98$

So, Percentage of students signed up for neither canoeing nor trekking is given by

$\dfrac{98}{180}\times 100\\\\=54.4\%\\\\\approx 54\%$

Hence,  Third option is correct.