Question

the conditional relative frequency table was calculated by row using data from a survey of one stations television programming. the survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period.
television programming

	live	recorded	total
children	0.5	0.5	1.0
total	≈0.583	≈0.417	1.0

which is the best description of the value 0.375 in the table?
○ given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
○ given that the program was recorded, there is a 37.5% chance that it was targeted at adults.
○ 37.5% of the programs are targeted at adults.
○ 37.5% of the programs are recorded.

Explanation:

Step1: Understand Conditional Relative Frequency

Conditional relative frequency by row means we look at each row (Adult, Children) as a separate group. For the "Adult" row, the values are for programs targeted at adults.

Step2: Analyze the 0.375 Value

In the "Adult" row, the "Recorded" column has 0.375. This means, within the group of adult - targeted programs (the row total is 1.0, representing all adult - targeted programs), the proportion of recorded programs is 0.375 or 37.5%. So it's the probability that a program is recorded given that it is targeted at adults.

Step3: Eliminate Other Options

• Option 2: To find the probability that a program is targeted at adults given it's recorded, we would use the "Recorded" column total and the "Adult" - "Recorded" value. The "Recorded" column total is approximately 0.417, and the "Adult" - "Recorded" value is 0.375. The conditional probability here would be $\frac{0.375}{0.417}\approx0.9$, not 0.375.
• Option 3: The proportion of programs targeted at adults is not 0.375. The total for adults is 1.0 (as a row total), but the overall proportion of adult - targeted programs would be calculated from the grand total. From the table, the total for adults is 1.0, children is 1.0, but the grand total is 1.0 (since it's a conditional relative frequency by row, but if we consider overall, we need to know the actual counts, but from the table's row - based conditional, the "Adult" row is about adult - targeted programs. The value 0.375 is not the proportion of adult - targeted programs overall.
• Option 4: The proportion of recorded programs is approximately 0.417 (from the "Total" row - "Recorded" column), not 0.375.

Answer:

Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.