Question

the science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition. what is the probability that both people chosen are females? \\(\frac{1}{90}\\) \\(\frac{1}{5}\\) \\(\frac{2}{9}\\) \\(\frac{1}{4}\\)

Explanation:

Step1: Calculate total students

Total students = 5 (females) + 5 (males) = 10.

Step2: Probability first is female

Probability first chosen is female: $\frac{5}{10}=\frac{1}{2}$.

Step3: Probability second is female (after first)

After choosing one female, 4 females left and 9 total. Probability: $\frac{4}{9}$.

Step4: Multiply probabilities (independent events in sequence)

Total probability = $\frac{1}{2} \times \frac{4}{9} = \frac{4}{18} = \frac{2}{9}$.

Answer:

$\frac{2}{9}$ (corresponding to the option with $\frac{2}{9}$)