Marcie conducts an experiment with a bag of marbles. She draws one marble from the bag, records its color, returns the marble to the bag, and draws again. The results of her experiment are shown below.

\begin{tabular}{|c|c|}
\hline Marble Color & \begin{tabular}{c}
Number of \\
Times Drawn
\end{tabular} \\
\hline red & 5 \\
\hline blue & 6 \\
\hline green & 4 \\
\hline purple & 1 \\
\hline yellow & 4 \\
\hline
\end{tabular}

Based on Marcie's experiment, what proportion of the marbles in the bag would she expect to be purple?

A. [tex]$5 \%$[/tex]
B. [tex]$1 \%$[/tex]
C. [tex]$20 \%$[/tex]
D. [tex]$10 \%$[/tex]



Answer :

Let's break down the problem step-by-step to find the proportion of purple marbles based on Marcie's experiment results.

1. Calculate the total number of draws:
- Red: 5
- Blue: 6
- Green: 4
- Purple: 1
- Yellow: 4

To find the total number of draws, we add these numbers together:
[tex]\[ 5 + 6 + 4 + 1 + 4 = 20 \][/tex]
So, the total number of draws is 20.

2. Determine the number of purple marbles drawn:
- According to the table, purple marbles were drawn 1 time.

3. Calculate the proportion of purple marbles:
- The proportion of purple marbles is the number of purple marbles drawn divided by the total number of draws.
[tex]\[ \text{Proportion of purple marbles} = \frac{1}{20} \][/tex]

4. Convert the proportion to a percentage:
- To convert the proportion to a percentage, we multiply by 100.
[tex]\[ \text{Proportion of purple marbles in percentage} = \left(\frac{1}{20}\right) \times 100 = 5\% \][/tex]

Therefore, based on Marcie's experiment, the proportion of the marbles in the bag that she would expect to be purple is [tex]\(5\%\)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{A. \ 5 \%} \][/tex]