Question

A school offers band and chorus classes. The table shows the percents of the 1200 students in the school who are enrolled in band, chorus, or neither class. How many students are enrolled in both classes?

Answer 1

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 $P(A) = 0.5$.

• 40% of the students involved in the chorus, hence $P(B) = 0.4$.

• 30% involved in neither, hence $1 - P(A \cup B) = 0.3 \rightarrow P(A \cup B) = 0.7$.

The percentage involved in both is:

$P(A \cap B) = P(A) + P(B) - P(A \cup B)$

Hence:

$P(A \cap B) = 0.5 + 0.4 - 0.7 = 0.2$

Then, out of 1200 students:

$0.2(1200) = 240$

240 students are enrolled in both classes.

To learn more about Venn probabilities, you can take a look at brainly.com/question/25698611