Question

in a certain school 40% of the pupils play basketball , 25% play volleyball , and 10% play basketball and volleyball . what percentage of the pupils in the school play neither play basketball nor volleyball . display with venn diagram

Answer 1

Let pupils playing basket ball = A= 40%
Pupils playing volleyball = B= 25 %
Pupils playing both basketball and volleyball = $A\cap B=10\%$
We know that ,
$$\begin{gathered} \mathrm{n}(\mathrm{A}\cup \mathrm{B})=\mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}(\mathrm{A}\cap \mathrm{B}) \\ \mathrm{Putting}\mathrm{value}\mathrm{we}\mathrm{get}, \\ \mathrm{n}(\mathrm{A}\cup \mathrm{B})=40+25-10=55\% \\ \mathrm{So}\mathrm{percentage}\mathrm{of}\mathrm{the}\mathrm{pupils}\mathrm{playing}\mathrm{neither}\mathrm{basketball}\mathrm{nor}\mathrm{volleyball} \\ =\mathrm{n}(\mathrm{A}\cup \mathrm{B})\text{'} \\ =\mathrm{U}-\mathrm{n}(\mathrm{A}\cup \mathrm{B})\text{'} \\ =100-55=45\% \end{gathered}$$