Let's analyze the problem step-by-step:
1. Given Values:
- Number of players who preferred coupon books: \( 12 \)
- Number of players who did not prefer coupon books (hence likely preferred magazines or neither): \( 19 \)
- Number of players who preferred both coupon books and magazines: \( 7 \)
2. Total Number of Surveyed Players:
To find the total number of surveyed players, we sum the number of players in each category:
[tex]\[
\text{Total Surveyed} = 12 + 19 + 7 = 38
\][/tex]
3. Calculate the Percentage of Players Who Preferred Coupon Books Only:
The number of players who preferred coupon books only can be found by subtracting the number of players who preferred both from the total number of players who preferred coupon books:
[tex]\[
\text{Coupon Books Only} = 12 - 7 = 5
\][/tex]
Now, we can calculate the relative frequency (percentage) of players who preferred coupon books only out of the total surveyed. This is done by dividing the number of players preferring coupon books only by the total number of surveyed players and then multiplying by 100:
[tex]\[
\text{Percentage} = \left( \frac{12}{38} \right) \times 100 \approx 31.57894736842105\%
\][/tex]
4. Round to the Nearest Whole Percent:
Rounding \( 31.57894736842105\% \) to the nearest whole percent gives:
[tex]\[
a = 32\%
\][/tex]
Thus, the correct value of \( a \) in the relative frequency table for the survey results is \( 32\% \), which does not correspond to any given options in the question. The question might contain an error in the provided options or the interpretation of the question. Based on our calculations, we can confidently state:
[tex]\[ \boxed{32\%} \][/tex]
