To find the probability of selecting students in the specified order — a girl, a boy, and then a girl — let's break down the steps and the corresponding probabilities for each selection:
1. The first student selected is a girl:
- There are 5 girls and 5 boys, making a total of 10 students.
- The probability of selecting a girl first is:
[tex]\[
\frac{\text{number of girls}}{\text{total number of students}} = \frac{5}{10} = 0.5
\][/tex]
2. The second student selected is a boy:
- After selecting one girl, we are left with 4 girls and 5 boys, making a total of 9 students remaining.
- The probability of selecting a boy next is:
[tex]\[
\frac{\text{number of boys}}{\text{remaining students}} = \frac{5}{9} \approx 0.5555555555555556
\][/tex]
3. The third student selected is a girl:
- After selecting the second student (a boy), we are now left with 4 girls and 4 boys, making a total of 8 students remaining.
- The probability of selecting another girl at this point is:
[tex]\[
\frac{\text{number of girls}}{\text{remaining students}} = \frac{4}{8} = 0.5
\][/tex]
4. Total probability:
- To find the overall probability, we multiply the probabilities of each step:
[tex]\[
\text{Total Probability} = \left(\frac{5}{10}\right) \times \left(\frac{5}{9}\right) \times \left(\frac{4}{8}\right) = 0.5 \times 0.5555555555555556 \times 0.5 \approx 0.1388888888888889
\][/tex]
This probability closely matches one of the given answer choices. Therefore, the correct answer is:
[tex]\[
\boxed{\frac{5}{36}}
\][/tex]
