A class has 20 girls and 16 boys. One student is selected at random. Find the probability that the student is a girl.

Answer

To find the probability that a randomly selected student from a class of 20 girls and 16 boys is a girl, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of girls and boys**:
- Number of girls = 20
- Number of boys = 16

2. **Calculate the total number of students**:
- Total number of students = Number of girls + Number of boys
- Total number of students = 20 + 16 = 36

3. **Determine the number of favorable outcomes**:
- The favorable outcome in this case is selecting a girl.
- Number of favorable outcomes (girls) = 20

4. **Use the probability formula**:
- The formula for probability is:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes is the number of girls (20) and the total number of outcomes is the total number of students (36).

5. **Substituting the values into the formula**:
\[ \text{Probability of selecting a girl} = \frac{20}{36} \]

6. **Simplify the fraction**:
- To simplify \(\frac{20}{36}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ \frac{20 \div 4}{36 \div 4} = \frac{5}{9} \]

7. **Conclusion**:
- Therefore, the probability that the student selected is a girl is \(\frac{5}{9}\).