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A random sample of people were asked about their preferences regarding decoration and their interest in fashion. Here are the characteristics of the sampled individuals:

- 150 people responded to the survey
- [tex]$70 \%$[/tex] of the responders do not pay attention to fashion
- 33 of the responders who prefer neutral decorations also do not pay attention to fashion
- 20 of the responders who pay attention to fashion also prefer colorful decorations in their homes

Use the provided characteristics to complete the two-way table on your own paper:

\begin{tabular}{|c|c|c|}
\hline
& \begin{tabular}{c}
prefer colorful \\
decorations
\end{tabular}
& \begin{tabular}{c}
prefer neutral \\
decorations
\end{tabular} \\
\hline
\begin{tabular}{c}
pay attention to \\
fashion
\end{tabular}
& \\
\hline
\begin{tabular}{c}
do not pay attention \\
to fashion
\end{tabular}
& & \\
\hline
\end{tabular}

Then use the table to answer the following question:
How many of the sampled people do not pay attention to fashion and prefer colorful decorations?



Answer :

GinnyAnswer
Sure, let's fill out the two-way table and solve the problem step-by-step.

Step 1: Calculate the number of people who do not pay attention to fashion.
- Total respondents: [tex]\(150\)[/tex]
- Percentage of respondents who do not pay attention to fashion: [tex]\(70\%\)[/tex]

Number of individuals who do not pay attention to fashion:
[tex]\[ 150 \times \frac{70}{100} = 105 \][/tex]

Step 2: Use the given information to fill in related parts of the table. Specifically:
- 33 of the responders who prefer neutral decorations also do not pay attention to fashion
- 20 of the responders who pay attention to fashion also prefer colorful decorations in their homes

Step 3: Calculate the number of people who do not pay attention to fashion and prefer colorful decorations.
- From the total of 105 respondents who do not pay attention to fashion, we subtract those who prefer neutral decorations (33):

Number of individuals who do not pay attention to fashion and prefer colorful decorations:
[tex]\[ 105 - 33 = 72 \][/tex]

The complete two-way table will look like this:
\begin{tabular}{|c|c|c|}
\hline & \begin{tabular}{c}
prefer colorful \\
decorations
\end{tabular} & \begin{tabular}{c}
prefer neutral \\
decorations
\end{tabular} \\
\hline \begin{tabular}{c}
pay attention to \\
fashion
\end{tabular} & 20 & \\
\hline \begin{tabular}{c}
do not pay attention \\
to fashion
\end{tabular} & 72 & 33 \\
\hline
\end{tabular}

Finally, the number of sampled people who do not pay attention to fashion and prefer colorful decorations is:
[tex]\[ 72 \][/tex]

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