To solve this problem, we need to determine the number of students who have a dog and then find the probability that a randomly chosen student has a dog.

1. **Identify the total number of students:**
- Total students = 23

2. **Identify the number of students who do not have a cat or a dog:**
- Students without a cat or a dog = 8

3. **Calculate the number of students who have either a cat or a dog or both:**
- Students with a cat or a dog or both = Total students - Students without a cat or a dog
- Students with a cat or a dog or both = 23 - 8 = 15

4. **Identify the number of students who have a cat:**
- Students with a cat = 8

5. **Identify the number of students who have a dog:**
- Students with a dog = 13

6. **Use the principle of inclusion-exclusion to find the number of students who have both a cat and a dog:**
- Students with both a cat and a dog = (Students with a cat) + (Students with a dog) - (Students with a cat or a dog or both)
- Students with both a cat and a dog = 8 + 13 - 15 = 6

7. **Calculate the number of students who have only a dog:**
- Students with only a dog = Students with a dog - Students with both a cat and a dog
- Students with only a dog = 13 - 6 = 7

8. **Calculate the total number of students who have a dog (either only a dog or both a dog and a cat):**
- Total students with a dog = Students with only a dog + Students with both a cat and a dog
- Total students with a dog = 7 + 6 = 13

9. **Calculate the probability that a randomly chosen student has a dog:**
- Probability = (Number of students with a dog) / (Total number of students)
- Probability = 13 / 23

Therefore, the probability that a student chosen randomly from the class has a dog is $ \frac{13}{23} $.

Question

To solve this problem, we need to determine the number of students who have a dog and then find the probability that a randomly chosen student has a dog.

1. **Identify the total number of students:**
   - Total students = 23

2. **Identify the number of students who do not have a cat or a dog:**
   - Students without a cat or a dog = 8

3. **Calculate the number of students who have either a cat or a dog or both:**
   - Students with a cat or a dog or both = Total students - Students without a cat or a dog
   - Students with a cat or a dog or both = 23 - 8 = 15

4. **Identify the number of students who have a cat:**
   - Students with a cat = 8

5. **Identify the number of students who have a dog:**
   - Students with a dog = 13

6. **Use the principle of inclusion-exclusion to find the number of students who have both a cat and a dog:**
   - Students with both a cat and a dog = (Students with a cat) + (Students with a dog) - (Students with a cat or a dog or both)
   - Students with both a cat and a dog = 8 + 13 - 15 = 6

7. **Calculate the number of students who have only a dog:**
   - Students with only a dog = Students with a dog - Students with both a cat and a dog
   - Students with only a dog = 13 - 6 = 7

8. **Calculate the total number of students who have a dog (either only a dog or both a dog and a cat):**
   - Total students with a dog = Students with only a dog + Students with both a cat and a dog
   - Total students with a dog = 7 + 6 = 13

9. **Calculate the probability that a randomly chosen student has a dog:**
   - Probability = (Number of students with a dog) / (Total number of students)
   - Probability = 13 / 23

Therefore, the probability that a student chosen randomly from the class has a dog is $ \frac{13}{23} $.

Knowee AI · Accepted Answer