Let's solve this step-by-step, filling in the band uniforms table with the appropriate values.
Given data:
- [tex]\( a = 33\% \)[/tex]
- [tex]\( b = 43\% \)[/tex]
- Gold and Blue uniforms [tex]\(\text{(Gold - Blue)} = 16\% \)[/tex]
- Not Blue and Not Gold uniforms [tex]\(\text{(Not Blue - Not Gold)} = 8\% \)[/tex]
1. Convert percentages to decimals for ease of calculation:
- [tex]\( a = 0.33 \)[/tex]
- [tex]\( b = 0.43 \)[/tex]
- Gold - Blue [tex]\( = 0.16 \)[/tex]
- Not Blue - Not Gold [tex]\( = 0.08 \)[/tex]
2. Fill in the given values in the table:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Band Uniforms} & \text{Blue} & \text{Not Blue} & \text{Total} \\
\hline
\text{Gold} & 0.16 & 0.33 & \\
\hline
\text{Not Gold} & 0.43 & 0.08 & \\
\hline
\text{Total} & & & 1 \\
\hline
\end{array}
\][/tex]
3. Calculate the total percentage for each row and column:
[tex]\[
\text{Total (Gold, Blue and Not Blue): } 0.16 + 0.33 = 0.49
\][/tex]
[tex]\[
\text{Total (Not Gold, Blue and Not Blue): } 0.43 + 0.08 = 0.51
\][/tex]
Thus, the complete table with all values filled in should be:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Band Uniforms} & \text{Blue} & \text{Not Blue} & \text{Total} \\
\hline
\text{Gold} & 0.16 & 0.33 & 0.49 \\
\hline
\text{Not Gold} & 0.43 & 0.08 & 0.51 \\
\hline
\text{Total} & 0.59 & 0.41 & 1 \\
\hline
\end{array}
\][/tex]
Here are the final values:
- [tex]\(\text{Gold - Blue} = 0.16\)[/tex]
- [tex]\(\text{Not Gold - Blue} = 0.43\)[/tex]
- [tex]\(\text{Gold - Not Blue} = 0.33\)[/tex]
- [tex]\(\text{Not Gold - Not Blue} = 0.08\)[/tex]
- [tex]\(\text{Total} = 1\)[/tex]
