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The problem is asking for the conditional probability that a student is a boy, given that they are a freshman.

To solve this, we use the formula for conditional probability:

\[
P(\text{Boy | Freshman}) = \frac{P(\text{Boy and Freshman})}{P(\text{Freshman})}
\]

### Step 1: Find \( P(\text{Boy and Freshman}) \)
From the table, the number of boys who are freshmen is 7.

### Step 2: Find \( P(\text{Freshman}) \)
The total number of freshmen (both boys and girls) is:
\[
7 \text{ (boys)} + 5 \text{ (girls)} = 12
\]

### Step 3: Compute the conditional probability
\[
P(\text{Boy | Freshman}) = \frac{7}{12}
\]

Thus, the probability that a student is a boy, given that they are a freshman, is:

\[
P(\text{Boy | Freshman}) = \frac{7}{12} \approx 0.5833
\]

Would you like more details on this solution or have any questions?

Here are some related questions you might explore:
1. What is the probability that a student is a girl, given that they are a freshman?
2. What is the total probability that a randomly selected student is a boy?
3. What is the probability that a student is a junior, given they are a boy?
4. What is the probability that a student is a sophomore, given that they are a girl?
5. How would the result change if more freshmen boys were added?

**Tip:** Conditional probability helps focus on a specific subgroup within the overall sample, making it useful in real-world situations where additional information is available.

A student is randomly selected from this table. What is the probability that they are a boy, given that they are a freshman?

Learn how to find the probability that a student is a boy given that they are a freshman using a conditional probability formula. The table shows a breakdown of students across grades. This problem is suitable for students in Grades 9-12 and focuses on calculating P(Boy | Freshman).

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