5. A group of 100 students are asked if they like folk music, rock music or soul music.
\begin{displayquote}
All students who like folk music also like rock music No students like both rock music and soul music 75 students do not like soul music 12 students who like rock music do not like folk music 30 students like folk music
- Draw a Venn diagram to illustrate this information.
- State two of these types of music that are mutually exclusive.
\end{displayquote}
Find the probability that a randomly chosen student
- does not like folk music, rock music or soul music,
- likes rock music,
- likes folk music or soul music.
Given that a randomly chosen student likes rock music,
- find the probability that he or she also likes folk music.