Question

mr. garcia has 15 boys and 10 girls in his math class. he selects two students at random to demonstrate how they solved the day’s challenge assignment. what is the probability that both students are girls?

Explanation:

Step1: Calculate total number of students

The total number of students is $15 + 10=25$.

Step2: Calculate probability of first - student being a girl

The probability that the first - selected student is a girl is $\frac{10}{25}=\frac{2}{5}$.

Step3: Calculate probability of second - student being a girl given first is a girl

After one girl is selected, there are 9 girls left and 24 students left. So the probability that the second - selected student is a girl given that the first one is a girl is $\frac{9}{24}=\frac{3}{8}$.

Step4: Calculate probability of both students being girls

By the multiplication rule of probability for dependent events, the probability that both students are girls is $\frac{2}{5}\times\frac{3}{8}=\frac{6}{40}=\frac{3}{20}$.

Answer:

$\frac{3}{20}$