Question

a college radio station surveyed 299 incoming freshmen to see how many like jazz 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.) all freshmen in the survey
(a) how many of the freshmen do not like jazz music? 155 freshmen
(b) how many of the freshmen like jazz music or classical music (or both)? freshmen
(c) how many of the freshmen like jazz music but do not like classical music? 41 freshmen

Explanation:

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

The total number of freshmen is \(41 + 103+33 + 122=299\). The number of freshmen who like jazz music is \(41+103 = 144\). So the number of freshmen who do not like jazz music is \(299-(41 + 103)=155\).

Step2: Find the number of freshmen who like jazz music or classical music

The number of freshmen who like jazz music is \(41+103\), the number of freshmen who like classical music is \(33 + 103\). Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(A\) is the set of freshmen who like jazz and \(B\) is the set of freshmen who like classical. So \(n(A\cup B)=(41 + 103)+(33+103)-103=41+103+33=177\).

Step3: Find the number of freshmen who like jazz music but do not like classical music

The number of freshmen who like jazz music is \(41+103\), and the number of freshmen who like both is \(103\). So the number of freshmen who like jazz but not classical is \(41\).

Answer:

(a) \(155\) freshmen
(b) \(177\) freshmen
(c) \(41\) freshmen