Question

a college radio station surveyed 420 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.) (a) how many of the freshmen like jazz music? freshmen (b) how many of the freshmen like neither jazz music nor classical music? freshmen (c) how many of the freshmen do not like both jazz music and classical music? freshmen

Explanation:

Step1: Find freshmen who like jazz

Add the number of freshmen who like only jazz and those who like both jazz and classical.
$31 + 223$

Step2: Calculate the result for (a)

$31+223 = 254$

Step3: Find freshmen who like neither

The number outside the two - circles represents freshmen who like neither. So it is 121.

Step4: Find freshmen who do not like both

Subtract the number of freshmen who like both from the total number of freshmen surveyed. First, find the total number of freshmen surveyed which is $31 + 223+45 + 121=420$. Then subtract the number of those who like both (223). So it is $420 - 223=197$.

Answer:

(a) 254 freshmen
(b) 121 freshmen
(c) 197 freshmen