Acampus radio station surveyed 500 students to determine the types of music they like. the survey revealed that 199 like rock, 155 like country, and 114 like jazz. moreover, 24 like rock and country, 23 like rock and jazz, 19 like country and jazz, and 8 like all three types of music. what is the probability that a randomly selected student likes country but not rock?

There are 24 who like both rock and country. There are 8 who like all 3 types, and these eight have been counted under the 24. This means that the number who like rock and country but not jazz is 24 - 8 = 16.
We are given a total of 155 who like country. We subtract the 16 who like both rock and country, and are left with 139 people who like country but not rock. (It does not matter whether they like jazz or not).
The probability is 155 out of the total of 500, so 155/500 = 31/100 = 0.31.