word problem

Question

A survey of 78 college students was taken to detemine the musical styles they liked. Of those, 37 students listened to rock, 33 to classical, and 32 to jazz. Also, 16 students listened to rock and jazz, 19 to rock and classical, and 14 to classical and jazz. Finally, 8 students listened to all three musical styles. Construct a Vdnn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions.

 

a. How many listened to only rock music? n(only rock)=

 

Answer 1

Hi Sav,

 

Ten listened to only rock music. Since I can not draw the Venn diagram here, I will describe it as best I can. Start by drawing 3 over lapping circles and label the part that is in all three with an 8. Since 16 listened to rock and jazz and 8 are already in that area which is in all three, we need to label an additional 8 in the area of rock and jazz but not in all three. Since 19 listen to rock and classical, we need to label an additional 11 in the area in common to rock and classical which is different from the area of all three. Since there are 37 that listen to rock and there are 8 , 8, and 11 already labeled in the rock area, that leaves 10 in the rock area that listen strictly to rock.