Question

a university conducted a survey to understand credit card usage among its students. the students were categorized based on their year: first year, second year, and third year. the survey also distinguished between students who pay their credit card balance in full each month and those who carry a balance. the total number of students surveyed was 600.
given a student carries a balance, what is the conditional relative frequency that they are a second year?

Explanation:

Step1: Recall the formula for conditional relative frequency

Conditional relative frequency \(=\frac{\text{Frequency of the joint event}}{\text{Frequency of the condition}}\)
Here, the joint event is "second - year and carry a balance", and the condition is "carry a balance".

Step2: Identify the frequencies from the table

The frequency of "second - year and carry a balance" is \(50\), and the frequency of "carry a balance" is \(200\)

Step3: Calculate the conditional relative frequency

\(\frac{50}{200}=0.25\)

Answer:

\(0.25\)