A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 205 like rock, 158 like country, and...

A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 205 like rock, 158 like country, and 120 like jazz. Moreover, 25 like rock and country, 27 like rock and jazz, 20 like country and jazz, and 7 like all three types of music. What is the probability that a randomly selected student likes neither rock nor country? Note: A Venn diagram may be useful here.