Question

the relative frequency table given describes students at a local high school, showing whether they are enrolled in an ap course or not and whether they are part of a club or not. table content: takes ap course, does not take ap course, total; in a club: 36%, 39%, 75%; not in a club: 4%, 21%, 25%; total: 40%, 60%, 100% what is the conditional relative frequency of being in a club given that you are in an ap course? options: 90%, 75%, 45%, 36%

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional relative frequency (conditional probability) is \( P(A|B)=\frac{P(A\cap B)}{P(B)} \). Here, event \( A \) is "in a club" and event \( B \) is "takes an AP course".

Step2: Identify Relevant Frequencies

From the table, the relative frequency of "takes AP course and is in a club" (\( P(A\cap B) \)) is \( 36\% \) (or \( 0.36 \)), and the relative frequency of "takes AP course" (\( P(B) \)) is \( 40\% \) (or \( 0.40 \)).

Step3: Calculate the Conditional Frequency

Using the formula, \( P(\text{in a club}|\text{takes AP course})=\frac{0.36}{0.40} = 0.9 = 90\% \).

Answer:

90%