Question

In a survey of $400$ students in a school, $100$ are listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking "Neither apple nor orange juice"

• A. $175$
• B. $225$
• C. $275$
• D. $noneofthese$

Answer 1

Answer: (B)

$225$

$Thereare400students.So,n\left(s\right)=400.$

$100studentstakeapplejuice,n\left(A\right)=100$

$150takeorangejuice,n\left(o\right)=150$

$75studentstakebothappleabdorangejuice,n(A\cap o)=75$

$So,n(A\cup o)=n\left(A\right)+n\left(o\right)-n(A\cap o)$

$=100+150-75$

$=175$

$Numberofstudentstakingneitherapplenororange$

$juice,n\left(\overline{A\cup o}\right)=n\left(s\right)-n(A\cup o)$

$=400-175$

$=225$