To determine the value of \( g \) in the relative frequency table, let's focus on finding the relative frequency of D given A.
The original frequency table shows:
| | C | D | Total |
|---|----|----|-------|
| A | 15 | 25 | 40 |
| B | 24 | 12 | 36 |
| Total | 39 | 37 | 76 |
First, we need to find the total frequency for D across all categories:
[tex]\[
\text{Total D} = 37
\][/tex]
Next, we identify the frequency of D given A, which is 25.
To calculate the relative frequency of D given A, we use the following formula:
[tex]\[
\text{Relative Frequency of D given A} = \left(\frac{\text{Frequency of D given A}}{\text{Total Frequency of D}}\right) \times 100
\][/tex]
Plugging in the values:
[tex]\[
\text{Relative Frequency of D given A} = \left(\frac{25}{76}\right) \times 100
\][/tex]
This calculation gives:
[tex]\[
\left(\frac{25}{76}\right) \times 100 = 32.89473684210527
\][/tex]
When rounded to the nearest percent, this value becomes:
[tex]\[
33\%
\][/tex]
Therefore, the value of \( g \) in the relative frequency table is:
[tex]\[
g = 33\%
\][/tex]
Hence, the correct answer is:
[tex]\[
33\%
\][/tex]
