Question

g.pr.10.1 (mc)

a study was conducted on 465 people to find their favorite genre of music. a two-way table below shows the results according to their age. find \\(p(\text{rock} \cup 36 - 50)\\).

\\(\

$$\begin{array}{c|c|c|c|c} & \\text{rock} & \\text{country} & \\text{pop} & \\text{hip-hop} \\\\ \\hline 10-19 & 10 & 22 & 45 & 32 \\\\ 20-35 & 29 & 30 & 40 & 25 \\\\ 36-50 & 30 & 28 & 38 & 20 \\\\ 51+ & 38 & 42 & 16 & 20 \\end{array}$$

\\)

• \\(\frac{28}{465}\\)
• \\(\frac{193}{465}\\)
• \\(\frac{238}{465}\\)
• \\(\frac{14}{31}\\)

Explanation:

Calculate individual and intersection counts

$$
LATEXBLOCK0
$$

Apply the addition rule for union probability

$$
LATEXBLOCK1
$$

Compute the final probability

$$ P(\text{Rock} \cup 36-50) = \frac{193}{465} $$

Answer:

• (A) \(\frac{28}{465}\)
• (B) \(\frac{193}{465}\) (Correct answer)
• (C) \(\frac{238}{465}\)
• (D) \(\frac{14}{31}\)