In a Mathematics class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an 'A grade student'?

Answer

To solve the problem, we need to find the probability of choosing a girl or an A grade student from a class of 30 students, where there are 17 boys and 13 girls, and 4 boys and 5 girls received an A grade.

### Step-by-Step Solution:

1. **Identify the total number of students**:
- Total students = 30

2. **Determine the number of girls**:
- Number of girls = 13

3. **Calculate the probability of selecting a girl**:
- Probability of selecting a girl = Number of girls / Total students
- Probability of selecting a girl = 13 / 30

4. **Determine the number of A grade students**:
- A grade students = 4 boys + 5 girls = 9 students

5. **Calculate the probability of selecting an A grade student**:
- Probability of selecting an A grade student = Number of A grade students / Total students
- Probability of selecting an A grade student = 9 / 30

6. **Use the principle of inclusion-exclusion**:
- Since the A grade girls are already counted in the total number of girls, we need to ensure we do not double count them.
- The number of A grade girls = 5
- The number of A grade boys = 4
- Therefore, the total number of unique A grade students = 9 (4 boys + 5 girls)

7. **Calculate the combined probability**:
- Probability of choosing a girl or an A grade student = Probability of a girl + Probability of an A grade student - Probability of an A grade girl
- Probability of choosing a girl or an A grade student = (13/30) + (9/30) - (5/30)
- Probability = (13 + 9 - 5) / 30 = 17 / 30

### Final Answer:
The probability of choosing a girl or an A grade student is **17/30**.