Question

At Lincoln High School, 25% of the students play on a sports team, and 13% of students play on a sports team and take a music class.



If one student chosen at random plays on a sports team, what is the probability that this student also takes a music class?

Answer options with 4 options
A.
12%

B.
19%

C.
38%

D.
52%

Answer 1

To find the probability that a student who plays on a sports team also takes a music class, we can use the conditional probability formula:

\[
P(M | S) = \frac{P(M \cap S)}{P(S)}
\]

Where:
- \(P(M | S)\) is the probability that a student takes a music class given that they play on a sports team.
- \(P(M \cap S)\) is the probability that a student plays on a sports team and takes a music class.
- \(P(S)\) is the probability that a student plays on a sports team.

From the problem:
- \(P(S) = 25\% = 0.25\)
- \(P(M \cap S) = 13\% = 0.13\)

Now we can substitute these values into the formula:

\[
P(M | S) = \frac{0.13}{0.25}
\]

Calculating this gives:

\[
P(M | S) = 0.52
\]

To convert this back into a percentage:

\[
P(M | S) = 0.52 \times 100 = 52\%
\]

Therefore, the probability that a student who plays on a sports team also takes a music class is \(52\%\).

The correct answer is **D. 52%**.