In a certain Algebra 2 class of 24 students, 11 of them play basketball and 15 of them play baseball. There are 7 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

To find the probability that a randomly chosen student from the class plays both basketball and baseball, we can use the principle of inclusion-exclusion.

Let's denote:
- \( n = 24 \) (total number of students),
- \( B = 11 \) (students who play basketball),
- \( A = 15 \) (students who play baseball),
- \( N = 7 \) (students who play neither sport).

First, we calculate the number of students who play at least one sport:

\[
\text{Students who play at least one sport} = n - N = 24 - 7 = 17
\]

Using the inclusion-exclusion principle, we have:

\[
\text{Students who play at least one sport} = B + A - x
\]
where \( x \) is the number of students who play both sports.

Setting up the equation:

\[
17 = 11 + 15 - x
\]

Solving for \( x \):

\[
17 = 26 - x \\
x = 26 - 17 = 9
\]

Thus, 9 students play both basketball and baseball.

Now, to find the probability that a randomly chosen student plays both sports, we use the formula for probability:

\[
P(\text{both}) = \frac{\text{Number of students who play both}}{\text{Total number of students}} = \frac{9}{24} = \frac{3}{8}
\]

Therefore, the probability that a randomly chosen student plays both basketball and baseball is \( \frac{3}{8} \).

### Summary
- Probability that a student plays both sports: \( \frac{3}{8} \)

Would you like more details or have any questions? Here are some related questions you might consider:
1. How many students play only basketball?
2. How many students play only baseball?
3. What is the probability that a student plays neither sport?
4. How would the probabilities change if more students joined the class?
5. Can we represent this situation using a Venn diagram? 

**Tip:** Understanding the inclusion-exclusion principle is crucial for solving problems involving overlapping sets.

Explore how to calculate the probability that a randomly chosen student from an Algebra 2 class plays both basketball and baseball. Given 24 students, 11 play basketball, 15 play baseball, and 7 play neither, the solution reveals that the probability is 3/8. Perfect for Grades 9-10.

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