https://file.aiquickdraw.com/mathbot/file/1729939550185gu6bwnd3.jpg

Let's go through each part of question (t) and question (u) from the image.

### Question (t) - Grade 11 Class Problem
1. **Information given:**
   - There are 30 students in total.
   - 16 of them are girls.
   - There are 7 girls with blue eyes and 6 boys with blue eyes.

#### Steps for Each Part:
1. **Draw a Venn Diagram:** 
   - Let:
     - \( G \) be the set of girls.
     - \( B \) be the set of students with blue eyes.
   - Use these sets to represent the 30 students, including overlapping areas where students are both girls and have blue eyes (7 girls with blue eyes).

2. **Find the probability that the class monitor is a girl:**
   \[
   P(\text{girl}) = \frac{\text{Number of girls}}{\text{Total number of students}} = \frac{16}{30}
   \]

3. **Find the probability that the class monitor is a boy with blue eyes:**
   \[
   P(\text{boy with blue eyes}) = \frac{\text{Number of boys with blue eyes}}{\text{Total number of students}} = \frac{6}{30}
   \]

4. **Find the probability that the class monitor has not got blue eyes:**
   - Total students with blue eyes = \( 7 + 6 = 13 \)
   \[
   P(\text{not blue eyes}) = 1 - \frac{13}{30} = \frac{17}{30}
   \]

5. **Find the probability that the class monitor is a girl and has not got blue eyes:**
   - Girls without blue eyes = Total girls - Girls with blue eyes = \( 16 - 7 = 9 \)
   \[
   P(\text{girl and not blue eyes}) = \frac{9}{30}
   \]

---

### Question (u) - Class of 40 Learners
1. **Information given:**
   - 25 take Science, 15 take Biology, and 16 take Geography.
   - 6 learners take both Geography and Computer Science.
   - 9 learners take Biology only, 7 take Science only, and 14 take Computer Science.

#### Steps for Each Part:
1. **Draw a Venn Diagram:** 
   - Represent each subject (Science, Geography, Biology, and Computer Science) as a circle in the Venn diagram.
   - Use the given numbers to fill in intersections.

2. **Find the probability that a randomly chosen learner takes Geography but not Computer Science:**
   - Calculate the number of students who take Geography but are not in Computer Science.
   - Probability:
     \[
     P(\text{Geography and not Computer Science}) = \frac{\text{Number of learners taking Geography only}}{40}
     \]

3. **Find the probability that a learner takes Science or Geography:**
   - Use the Venn diagram and include the union of Science and Geography.
   - Probability:
     \[
     P(\text{Science or Geography}) = \frac{\text{Number of learners in Science or Geography}}{40}
     \]

Let me know if you'd like detailed solutions for each probability calculation or need help with the Venn diagrams! 

---

### Follow-up Questions:
1. What is the probability of selecting a student who has both blue eyes and is a girl?
2. How would the probabilities change if one more boy with blue eyes joined the class?
3. If a student is chosen who does not have blue eyes, what is the probability they are a girl?
4. In question (u), how would the probability calculations change if 5 learners dropped Science?
5. What if there’s an overlap between learners in Science, Biology, and Geography? How does that affect the Venn diagram?

**Tip:** When constructing a Venn diagram, start with the intersections given and work outward to avoid miscounting overlaps.

In a Grade 11 class of 30 students, there are 16 girls, 7 girls with blue eyes, and 6 boys with blue eyes. A student is chosen at random to be the class monitor. (1) Draw a Venn diagram to represent the information. (2) Find the probability that the class monitor is a girl. (3) Find the probability that the class monitor is a boy with blue eyes. (4) Find the probability that the class monitor does not have blue eyes. (5) Find the probability that the class monitor is a girl and does not have blue eyes.

Solve a probability problem involving blue eyes and gender in a Grade 11 class. Learn to calculate probabilities using a Venn diagram, including probabilities for specific gender and eye color combinations, and complementary probabilities for students without blue eyes.

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