Answer:
55% of students don't prefer either trance nor dubstep.
Explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that a club goer prefers trance music.
B is the probability that a club goer prefers dubstep.
C is the probability that a club goer does not like any of these.
We have that:
In which a is the probability that a club goer likes trance music and not dubtep and
is the probability that a club goer likes both of these styles
By the same logic, we have that:
Either a person likes at least one these styles, or they prefer other styles. The sum of these probabilities is decimal 1. So:
We want to find C to solve this question. So
In which
15% preferred both trance and dubstep
This means that
25% prefer dubstep
This means that
35% of club goers prefer trance music
What percent of students don't prefer either trance nor dubstep
55% of students don't prefer either trance nor dubstep.