Question

a teacher is sorting students into teams by placing everyones name into a bowl. there are 15 girls and 9 boys in the class.

what is the probability that the first two names drawn are boys?

a.) \\(\frac{3}{23}\\)

b.) \\(\frac{27}{184}\\)

c.) \\(\frac{11}{31}\\)

d.) \\(\frac{1}{8}\\)

Explanation:

Calculate total students and first draw probability

Using the Theoretical Probability knowledge point

$$ \text{Total students} = 15 \text{ girls} + 9 \text{ boys} = 24 $$

$$ P(\text{First is a boy}) = \frac{9}{24} = \frac{3}{8} $$

Calculate second draw probability

Using the Theoretical Probability knowledge point

$$ \text{Remaining boys} = 8,\quad \text{Remaining total} = 23 $$

$$ P(\text{Second is a boy} \mid \text{First is a boy}) = \frac{8}{23} $$

Calculate joint probability of dependent events

Using the Independent Events Probability knowledge point

$$ P(\text{Both are boys}) = \frac{9}{24} \times \frac{8}{23} = \frac{3}{8} \times \frac{8}{23} = \frac{3}{23} $$

Answer:

• (a) \(\frac{3}{23}\) (Correct answer)
• (b) \(\frac{27}{184}\)
• (c) \(\frac{11}{31}\)
• (d) \(\frac{1}{8}\)