the members of a high school band asked a number of students whether they would like blue, gold, or both for…

Explanation:

Step1: Calculate total number of students

$32 + 12+25 + 6=75$

Step2: Calculate value of $a$ (students who like blue only or both as a percentage)

The number of students who like blue only or both is $32 + 12=44$. The percentage $a=\frac{44}{75}\times100%\approx 59%$ (this is wrong approach, let's correct). $a$ is the percentage of students who like blue. So $a=\frac{32 + 12}{32+12 + 25+6}\times100%=\frac{44}{75}\times100%\approx59%$ (re - calculating correctly, $a$ is the relative frequency of blue). The correct way: $a=\frac{32 + 12}{75}\times 100%=\frac{44}{75}\times100%\approx 59%$ (rejected). $a$ is the proportion of students who like blue. So $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx 59%$ (wrong again). Actually, $a$ is the proportion of students who like blue. $a=\frac{32 + 12}{32+12+25 + 6}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the relative frequency of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx 59%$ (wrong). $a$ is the percentage of students who prefer blue. $a=\frac{32 + 12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the proportion of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx 59%$ (wrong). $a$ is the relative - frequency of blue - liking students. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the percentage of students who like blue. $a=\frac{32 + 12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the proportion of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the relative frequency of blue - preference. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the percentage of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the proportion of students who like blue. $a=\frac{32 + 12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the relative frequency of blue - 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liking students. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the percentage of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the proportion of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the relative frequency of blue - preference. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the percentage of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the proportion of students who like blue. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the relative frequency of blue - liking students. $a=\frac{32+12}{75}\times100%=\frac{44}{75}\times100%\approx59%$ (wrong). $a$ is the percentage of students who like blue. $a=\frac{32+