Respuesta :
Answer:
37 students were in the class.
Step-by-step explanation:
We solve this problem building the Venn's diagram of these values.
I am going to say that:
A is the number of students who liked Hitchcock movies.
B is the number of students who liked Spielberg movies.
C is the probability that a mean is neither of those.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the number of students who liked Hitchcock movies but not Spielberg's and [tex]A \cap B[/tex] is the number of students who like both Hitchcock and Spielberg movies.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
How many students were in the class if every students is represented in the survey
This is
[tex](A \cup B) = a + b + (A \cap B)[/tex]
17 students who liked both kinds of films.
This means that [tex]A \cap B = 17[/tex]
21 students who liked Spielberg movies
This means that [tex]B = 21[/tex]. So:
[tex]B = b + (A \cap B)[/tex]
[tex]21 = b + 17[/tex]
[tex]b = 4[/tex]
33 students who liked Hitchcock movies
This means that [tex]A = 33[/tex]. So:
[tex]A = a + (A \cap B)[/tex]
[tex]33 = a + 17[/tex]
[tex]a = 16[/tex]
Finally
[tex](A \cup B) = a + b + (A \cap B) = 16 + 4 + 17 = 37[/tex]
37 students were in the class.
