Question

a) How many students play an instrument and play a sport?b) what fraction of students do not play sports?c) What fraction of students do not play sports but play an instrument?d) What fraction of sports playing students play an instrument?

Answer 1

a. The number of student that play an instrument and a sport is 23.

b. The fraction of student that do not play sports can be calculated below

$\begin{gathered} \text{total number that play sport = 23 + 15=38} \\ \text{total number that do not play sport =18+4=22} \\ \text{total number = 38+22=60 } \\ \text{fraction that do not play sport = }\frac{22}{60}=\frac{11}{30} \end{gathered}$

c. The fraction of students that do not play sports but play an instrument can be computed below

$\text{fractions that do not play sport but play instrument = }\frac{18}{60}=\frac{6}{20}=\frac{3}{10}$

d. The fraction of sport playing students that play instrument can be computed below

$\begin{gathered} \text{the fraction of sport playing student that play an instrument= }\frac{23}{41} \\ \end{gathered}$