applying the general multiplication rule\nthe science club has five female and five male students. the club…

applying the general multiplication rule\nthe science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition.\nwhat is the probability that both people chosen are females?\n$\frac{1}{90}$\n$\frac{1}{5}$\n$\frac{2}{9}$\n$\frac{1}{4}$

applying the general multiplication rule\nthe science club has five female and five male students. the club will randomly select two people to compete in the upcoming science competition.\nwhat is the probability that both people chosen are females?\n$\frac{1}{90}$\n$\frac{1}{5}$\n$\frac{2}{9}$\n$\frac{1}{4}$

Answer

Explanation:

Step1: Calculate probability of first - pick

The total number of students is (5 + 5=10). The number of female students is 5. The probability of picking a female student on the first pick is (\frac{5}{10}=\frac{1}{2}).

Step2: Calculate probability of second - pick

After picking a female student on the first pick, there are 4 female students left and 9 students in total. So the probability of picking a female student on the second pick is (\frac{4}{9}).

Step3: Use multiplication rule

By the multiplication rule of probability for independent - like events (in the sense of sequential selection without replacement), the probability that both people chosen are females is (\frac{1}{2}\times\frac{4}{9}=\frac{4}{18}=\frac{2}{9}).

Answer:

(\frac{2}{9})