Probability of Music Genre Preference

A survey was conducted among 200 students to determine their preferences for types of music they listen to. The results indicated that 120 students favored pop music, 90 students favored rock music, and 70 students favored classical music. Some students expressed a preference for more than one genre. Specifically, 30 students liked both pop and rock, 20 liked both pop and classical, and 10 liked both rock and classical. Additionally, 5 students liked all three genres.

What is the probability that a randomly selected student from this survey listens to at least one type of the three genres of music?