A campus radio station surveyed 190 students to determine the types of music the
ID: 3230183 • Letter: A
Question
A campus radio station surveyed 190 students to determine the types of music they liked. The survey revealed that 114 liked rock, 50 liked country, and 41 liked classical. Moreover, 14 liked rock and country, 15 liked rock and classical, and 11 liked classical and country, and 5;liked all three types of music. a) How many liked rock only? b) How many students liked classical and country but not rock? c) How many students like classical or country but not rock? d) How many like exactly one type of music? e) How many like exactly two types of music?Explanation / Answer
12.
n = 190
nrock = 114
ncountry = 40
nclassical = 41
nrock&country = 14
nrockclassical = 15
nclassical&country = 11
nall = 5
a. nonlyrock = 114-14-15+5 = 90
b. n classical and coutnry not rock = 14-5 =9
c. n classical or country but not rock = 50+41-11-15-14+5 = 56
d. n (only 1) = 190-15-14-11+2*5 = 160
e. n exactly 2 types of mucisc = 15+14+11-2*5 = 30
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