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? 1/90 1/5 2/9 1/4

Explanation:

Step1: Calculate the total number of students

There are \(5 + 5=10\) students in total.

Step2: Calculate the probability of choosing the first female

The probability of choosing the first female is \(\frac{5}{10}=\frac{1}{2}\).

Step3: Calculate the probability of choosing the second female

After choosing one female, there are \(4\) females left and \(9\) students left. So the probability of choosing the second female is \(\frac{4}{9}\).

Step4: Calculate the combined probability

Using the multiplication rule for independent events (in a sequential - without - replacement selection), the probability that both are females is \(\frac{5}{10}\times\frac{4}{9}=\frac{20}{90}=\frac{2}{9}\).

Answer:

\(\frac{2}{9}\) (the third option)