In a second grade class containing 12 girls and 9 boys, 2 students are selected at random to give out the math papers. What is the probability that both are girls? \( \frac{4}{7} \cdot \frac{4}{7} \) \( \frac{4}{7} \cdot \frac{11}{20} \) \( \frac{4}{7} \cdot \frac{3}{5} \) \( \frac{3}{7} \cdot \frac{2}{5} \)

To find the probability that both selected students are girls, we need to calculate the probability of selecting a girl on the first draw and then the probability of selecting a girl on the second draw. Given: - Total number of students in the class = 12 girls + 9 boys = 21 students - Number of girls in the class = 12 Probability of selecting a girl on the first draw = Number of girls / Total number of students = 12/21 Probability of selecting a girl on the second draw = Number of girls remaining / Total number of students remaining = 11/20 Therefore, the probability that both selected students are girls is the product of the probabilities of selecting a girl on the first and second draws: \[ \text{Probability} = \frac{12}{21} \times \frac{11}{20} \] Let's calculate this. Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{12}{21}\times 11}{20}\) - step1: Reduce the fraction: \(\frac{\frac{4}{7}\times 11}{20}\) - step2: Multiply the numbers: \(\frac{\frac{44}{7}}{20}\) - step3: Multiply by the reciprocal: \(\frac{44}{7}\times \frac{1}{20}\) - step4: Reduce the numbers: \(\frac{11}{7}\times \frac{1}{5}\) - step5: Multiply the fractions: \(\frac{11}{7\times 5}\) - step6: Multiply: \(\frac{11}{35}\) The probability that both selected students are girls is \( \frac{11}{35} \) or approximately 0.3142857.