Question

a college radio station surveyed 210 incoming freshmen to see how many like rap music and how many like classical music. the venn diagram below shows the results. (each number gives the number of freshmen who fall into that venn diagram category.) (a) how many of the freshmen do not like rap music? freshmen (b) how many of the freshmen like rap music or classical music (or both)? freshmen (c) how many of the freshmen like rap music but do not like classical music? freshmen

Explanation:

Step1: Find non - rap likers

Non - rap likers are those in the "like classical only" and "like neither" regions. So we add the number of students in those regions.
$49 + 48=97$

Step2: Find rap or classical likers

We add the number of students in the "like rap only", "like classical only" and "like both" regions.
$26+87 + 49=162$

Step3: Find rap but not classical likers

The number of students who like rap but not classical is the number in the "like rap only" region, which is 26.

Answer:

(a) 97 freshmen
(b) 162 freshmen
(c) 26 freshmen