Respuesta :
Using Venn probabilities, it is found that 240 students are enrolled in both classes.
Venn probabilities:
The events are:
- Event A: A student is enrolled in band.
- Event B: A student is enrolled in chorus.
The supposed percentages, which also represents the probabilities involving a single student, are:
- 50% of the students involved in the band, hence [tex]P(A) = 0.5[/tex].
- 40% of the students involved in the chorus, hence [tex]P(B) = 0.4[/tex].
- 30% involved in neither, hence [tex]1 - P(A \cup B) = 0.3 \rightarrow P(A \cup B) = 0.7[/tex].
The percentage involved in both is:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
Hence:
[tex]P(A \cap B) = 0.5 + 0.4 - 0.7 = 0.2[/tex]
Then, out of 1200 students:
[tex]0.2(1200) = 240[/tex]
240 students are enrolled in both classes.
To learn more about Venn probabilities, you can take a look at https://brainly.com/question/25698611
