Question

a college radio station surveyed 415 incoming freshmen to see how many like jazz music and how many like rap 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 both jazz music and rap music? freshmen (c) how many of the freshmen like jazz music or rap music (or both)? freshmen

Explanation:

Step1: Find the number of freshmen who do not like rap music

The number of freshmen who do not like rap music is the sum of those who only like jazz and those who like neither.
$196 + 56$

Step2: Find the number of freshmen who like both jazz and rap music

This is directly given by the intersection of the two circles in the Venn - diagram.
$75$

Step3: Find the number of freshmen who like jazz or rap (or both)

This is the sum of those who only like jazz, only like rap, and like both.
$196+75 + 88$

Answer:

(a) $252$ freshmen
(b) $75$ freshmen
(c) $359$ freshmen