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Let's solve this step-by-step.

**Given Data Table:**

|          | Freshman | Sophomore | Junior | Senior | Total |
|----------|----------|-----------|--------|--------|-------|
| Male     | 30       | 31        | 24     | 25     | 110   |
| Female   | 43       | 26        | 18     | 32     | 119   |
| **Total**| 73       | 57        | 42     | 57     | 229   |

### Part (a): Probability that the student is male or a junior

To find the probability of a student being male or a junior, we can use the formula for the probability of the union of two events:
\[
P(\text{Male or Junior}) = P(\text{Male}) + P(\text{Junior}) - P(\text{Male and Junior})
\]

1. **Calculate \( P(\text{Male}) \):**
   \[
   P(\text{Male}) = \frac{\text{Total Male Students}}{\text{Total Students}} = \frac{110}{229}
   \]

2. **Calculate \( P(\text{Junior}) \):**
   \[
   P(\text{Junior}) = \frac{\text{Total Juniors}}{\text{Total Students}} = \frac{42}{229}
   \]

3. **Calculate \( P(\text{Male and Junior}) \):**
   \[
   P(\text{Male and Junior}) = \frac{\text{Number of Male Juniors}}{\text{Total Students}} = \frac{24}{229}
   \]

4. **Combine the probabilities:**
   \[
   P(\text{Male or Junior}) = \frac{110}{229} + \frac{42}{229} - \frac{24}{229} = \frac{128}{229} \approx 0.56
   \]

So, the probability that the student is male or a junior is **0.56**.

### Part (b): Probability that the student is a freshman, given that the student is female

For this conditional probability, we use the formula:
\[
P(\text{Freshman | Female}) = \frac{P(\text{Freshman and Female})}{P(\text{Female})}
\]

1. **Calculate \( P(\text{Female}) \):**
   \[
   P(\text{Female}) = \frac{\text{Total Female Students}}{\text{Total Students}} = \frac{119}{229}
   \]

2. **Calculate \( P(\text{Freshman and Female}) \):**
   \[
   P(\text{Freshman and Female}) = \frac{\text{Number of Female Freshmen}}{\text{Total Students}} = \frac{43}{229}
   \]

3. **Combine the probabilities:**
   \[
   P(\text{Freshman | Female}) = \frac{43}{119} \approx 0.36
   \]

Thus, the probability that the student is a freshman, given that the student is female, is **0.36**.

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### Related Questions
1. What is the probability that a randomly selected student is female or a senior?
2. What is the probability that a randomly selected student is sophomore, given that the student is male?
3. What is the probability that the student is both male and a senior?
4. What is the probability that a student is female, given that the student is a freshman?
5. How many total students are either freshmen or juniors?

### Tip
When working with probability tables, carefully determine if you need joint (and), marginal (or), or conditional probabilities based on the question asked.

Suppose a student from the high school band is chosen at random. What is the probability that the student is male or a junior? What is the probability that the student is a freshman, given that the student is female?

Calculate the probability that a randomly chosen student is either male or a junior, and determine the conditional probability that a student is a freshman given they are female. Explore probability concepts with a high school band example, including the addition rule and conditional probability.

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