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To solve part (a), we need to find the conditional probability that a randomly selected student is male, given that the student is a nursing major.

The conditional probability formula is:
\[
P(\text{Male} \mid \text{Nursing Major}) = \frac{\text{Number of Male Nursing Majors}}{\text{Total Number of Nursing Majors}}
\]

### Step-by-Step Solution for Part (a)
1. **Identify the number of male nursing majors**: From the table, we see there are \(90\) male nursing majors.
2. **Identify the total number of nursing majors**: The total for nursing majors (both male and female) is \(816\).

Using the formula:
\[
P(\text{Male} \mid \text{Nursing Major}) = \frac{90}{816}
\]

3. **Calculate the probability**:
\[
P(\text{Male} \mid \text{Nursing Major}) = \frac{90}{816} \approx 0.110
\]

### Answer for Part (a)
The probability that a randomly selected student is male, given that the student is a nursing major, is approximately **0.110** (rounded to three decimal places).

Would you like details on part (b) or have any questions about this calculation?

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**Related Questions:**
1. How do we calculate conditional probability if we know the probability of both independent events?
2. What is the probability of selecting a female student given that the student is a nursing major?
3. How can we interpret conditional probability in real-world scenarios?
4. What would be the probability of selecting a non-nursing major, given that the student is female?
5. How do we calculate joint probabilities for categories with overlapping attributes?

**Tip:** Always make sure to use the correct subset when calculating conditional probabilities to avoid errors.

Find the probability that a randomly selected student is male, given that the student is a nursing major, based on the table data.

Learn how to calculate the conditional probability of a student being male given they are a nursing major. The problem uses conditional probability formulas to analyze data from a university’s student enrollment table, distinguishing between nursing and non-nursing majors by gender.

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