Question

A survey of college students finds that 35% like country music, 25% like gospel music, and 15% like both.

What is the proportion of students that like country music alone (no gospel music)?

What is the proportion of students that like gospel music alone (no country music)?

What is the proportion of students that like either country music or gospel music?

What is the proportion of students that like neither country music nor gospel music?

Answer format is .##

Answer 1

P(C) = 0.35

P(G) = 0.10

proportion of students that like country music alone (no gospel music) =P(C) - P(C G) = 0.35- 0.15 = 0.20 or 20%

proportion of students that like gospel music alone (no country music) = P(G) - P(C G) = 0.25- 0.15 = 0.10 or 10%

proportion of students that like either country music or gospel music = P(C)+ P(G) - P(C G) = 0.35 + 0.25- 0.15 = 0.45 or 45%

proportion of students that like neither country music nor gospel music =1- 0.45 = 0.55 or 55%