A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 198 like rock, 152 like country, and 113 like jazz. Moreover, 21 like rock and country, 22 like rock and jazz, 16 like country and jazz, and 5 like all three types of music. What is the probability that a radomly selected student likes jazz or country but not rock?

The probability that a randomly selected student likes jazz or country but not rock is 0.422.

Step-by-step explanation:

The information provided is:

Total number of students selected, N = 500.

The number of students who like rock, n (R) = 198.

The number of students who like country, n (C) = 152.

The number of students who like jazz, n (J) = 113.

The number of students who like rock and country, n (R ∩ C) = 21.

The number of students who like rock and Jazz, n (R ∩ J) = 22.

The number of students who like country and jazz, n (C ∩ J) = 16.

The number of students who like all three, n (R ∩ C ∩ J) = 5.

Consider the Venn diagram below.

Compute the probability that a randomly selected student likes jazz or country but not rock as follows:

P (J ∪ C ∪ not R) = P (Only J) + P (Only C) + P (Only J ∩ C)

Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.

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