Respuesta :
Answer:
55% of students don't prefer either trance nor dubstep.
Step-by-step 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:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a club goer likes trance music and not dubtep and [tex]A \cap B[/tex] is the probability that a club goer likes both of these styles
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
Either a person likes at least one these styles, or they prefer other styles. The sum of these probabilities is decimal 1. So:
[tex]P(A \cup B) + C = 1[/tex]
We want to find C to solve this question. So
[tex]C = 1 - P(A \cup B)[/tex]
In which
[tex]P(A \cup B) = a + b + (A \cap B)[/tex]
15% preferred both trance and dubstep
This means that [tex]A \cap B = 0.15[/tex]
25% prefer dubstep
This means that [tex]B = 0.25[/tex]
[tex]B = b + (A \cap B)[/tex]
[tex]0.25 = b + 0.15[/tex]
[tex]b = 0.10[/tex]
35% of club goers prefer trance music
[tex]A = a + (A \cap B)[/tex]
[tex]0.35 = a + 0.15[/tex]
[tex]a = 0.20[/tex]
What percent of students don't prefer either trance nor dubstep
[tex]P(A \cup B) = a + b + (A \cap B) = 0.20 + 0.10 + 0.15 = 0.45[/tex]
[tex]C = 1 - P(A \cup B) = 1-0.45 = 0.55[/tex]
55% of students don't prefer either trance nor dubstep.
