Statistics question.. not too hard but I'm not sure what the answer is :o)?

Musical styles other than rock and pop are becoming more popular. A survey of college students finds that 30% like country music, 50% like gospel music, and 20% like both.

(a) Make a Venn diagram with these results. (Do this on paper. Your instructor may ask you to turn in your work.)

(b) What percent of college students like country but not gospel?

%

(c) What percent like neither country nor gospel?

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• stym
Lv 5

a) Draw a big circle. This is the set of your students.

Inside the big circle, draw two smaller circles that intersect.

One of them is the set of students who like country, the other is the set of students who like gospel.

The "like country" set has a size of 0.3, the "like gospel" set has a size of 0.5 and the "Students" set has a size of 1.

the size of the intersection of the two small sets is 0.2.

b) That is the size of your "like country" set minus the size of the intersection of "like country" and "like gospel"

0.3-0.2 = 0.1 10% of students like country but not gospel.

c) That is the area in your big circle that is outside the two smaller circles and their intersection.

size of your Students set minus (size of"like gospel" +

size of "like country" - size of intersection) = 1 - (0.5+0.3-0.2) = 0.4

40% of the students like neither gospel nor country.

You subtract the size of the intersection because it is counted twice when you add the size of the two small circles. The Venn diagram really helps understanding the problem.