Answer:
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, <em>N</em> = 500.
The number of students who like rock, <em>n</em> (<em>R</em>) = 198.
The number of students who like country, <em>n</em> (<em>C</em>) = 152.
The number of students who like jazz, <em>n</em> (<em>J</em>) = 113.
The number of students who like rock and country, <em>n</em> (<em>R </em>∩ <em>C</em>) = 21.
The number of students who like rock and Jazz, <em>n</em> (<em>R </em>∩ <em>J</em>) = 22.
The number of students who like country and jazz, <em>n</em> (<em>C </em>∩ <em>J</em>) = 16.
The number of students who like all three, <em>n</em> (<em>R </em>∩ <em>C </em>∩ <em>J</em>) = 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)
![=\frac{80}{500}+\frac{120}{500}+\frac{11}{500}\\=\frac{211}{500}\\=0.422](https://tex.z-dn.net/?f=%3D%5Cfrac%7B80%7D%7B500%7D%2B%5Cfrac%7B120%7D%7B500%7D%2B%5Cfrac%7B11%7D%7B500%7D%5C%5C%3D%5Cfrac%7B211%7D%7B500%7D%5C%5C%3D0.422)
Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.