Question

determine $p(\text{junior} | \text{pop})$. enter the answer in the space provided. use numbers instead of words. the table is about favorite type of music with rows as grade level (sophomore, junior, total) and columns as hip hop, country, pop, total. the data: sophomore: hip hop 21, country 10, pop 4, total 35; junior: hip hop 9, country 14, pop 12, total 35; total: hip hop 30, country 24, pop 16, total 70. question 2 of 4

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). In the context of a two - way table, if \( A \) is "junior" and \( B \) is "pop", then \( n(A\cap B) \) (the number of students who are junior and like pop) and \( n(B) \) (the number of students who like pop) can be found from the table. The formula can also be written as \( P(\text{junior}|\text{pop})=\frac{\text{Number of juniors who like pop}}{\text{Total number of students who like pop}} \).

Step2: Identify Values from the Table

From the table, the number of juniors who like pop is \( 12 \), and the total number of students who like pop is \( 16 \).

Step3: Calculate the Probability

\( P(\text{junior}|\text{pop})=\frac{12}{16} = 0.75 \). To convert this to a percentage, we multiply by \( 100 \), so \( 0.75\times100 = 75\% \).

Answer:

75