Question

applying the general multiplication rule

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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:

Calculate the probability of selecting the first female student

Using the Dependent Events and Probability Multiplication Rule knowledge points

$$ P(F_1) = \frac{5}{10} = \frac{1}{2} $$

Calculate the probability of selecting the second female student

Using the Dependent Events and Probability Multiplication Rule knowledge points

$$ P(F_2 \mid F_1) = \frac{4}{9} $$

Calculate the joint probability of both selections

Using the Probability Multiplication Rule knowledge point

$$ P(F_1 \cap F_2) = P(F_1) \times P(F_2 \mid F_1) = \frac{1}{2} \times \frac{4}{9} = \frac{2}{9} $$

Answer:

• (A) \(\frac{1}{90}\)
• (B) \(\frac{1}{5}\)
• (C) \(\frac{2}{9}\) (Correct answer)
• (D) \(\frac{1}{4}\)