Question

(a) how many of the freshmen like rock but dont like classical?
(b) how many of the freshmen like neither jazz nor rock?
(c) how many of the freshmen like exactly one of the three types of music?

Explanation:

Step1: Find the number of freshmen who like rock but not classical

From the Venn - diagram, the regions that represent freshmen who like rock but not classical are the part of the rock circle that does not overlap with the classical circle.
The value is \(131 + 53=184\)

Step2: Find the number of freshmen who like neither jazz nor rock

The region that represents freshmen who like neither jazz nor rock is the region outside the rock and jazz circles.
The value is \(46+143 + 41=230\)

Step3: Find the number of freshmen who like exactly one of the three types of music

The regions for exactly one type:

• Only rock: \(131\)
• Only classical: \(143\)
• Only jazz: \(67\)

The sum is \(131+143 + 67=341\)

Answer:

(a) \(184\)
(b) \(230\)
(c) \(341\)