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Let's solve the problem step by step:

We are given:
- A class of 30 students.
- 11 students play basketball.
- 9 students play baseball.
- 15 students play neither sport.

We are asked to find the probability that a randomly chosen student plays both basketball and baseball.

### Step 1: Determine the number of students who play either or both sports.
If 15 students play neither sport, then:
\[
\text{Number of students who play either or both sports} = 30 - 15 = 15.
\]

### Step 2: Use the principle of inclusion-exclusion.
We know:
- 11 students play basketball.
- 9 students play baseball.

Let \( x \) represent the number of students who play both basketball and baseball.

The inclusion-exclusion formula for the number of students who play either basketball or baseball is:
\[
\text{Number who play either or both sports} = (\text{Number who play basketball}) + (\text{Number who play baseball}) - (\text{Number who play both sports}).
\]
Substituting the known values:
\[
15 = 11 + 9 - x.
\]
Solving for \( x \):
\[
15 = 20 - x \quad \Rightarrow \quad x = 5.
\]
So, 5 students play both basketball and baseball.

### Step 3: Calculate the probability.
The probability that a randomly chosen student plays both basketball and baseball is:
\[
P(\text{both sports}) = \frac{\text{Number who play both sports}}{\text{Total number of students}} = \frac{5}{30} = \frac{1}{6}.
\]

Thus, the probability is \( \frac{1}{6} \).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What is the probability that a randomly chosen student plays only basketball?
2. How many students play only baseball?
3. What is the probability that a randomly chosen student plays neither sport?
4. Can the inclusion-exclusion principle be applied to more than two sets?
5. What would happen to the probability if the number of students who play both sports increased?

**Tip:** When dealing with probability, always make sure to account for the total population and consider overlaps carefully when using the inclusion-exclusion principle.

In a certain Algebra 2 class of 30 students, 11 of them play basketball and 9 of them play baseball. There are 15 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Learn how to calculate the probability that a student from a class of 30 plays both basketball and baseball. This problem involves using the inclusion-exclusion principle to find the number of students who play both sports. Suitable for students in Grades 9-11.

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