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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]$20\%$[/tex]

B. [tex]$10\%$[/tex]

C. [tex]$1\%$[/tex]

D. [tex]$5\%$[/tex]

Sagot :

GinnyAnswer
To find the proportion of purple marbles based on Marcie's experiment, follow these steps:

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

Total marbles = 5 (red) + 6 (blue) + 4 (green) + 1 (purple) + 4 (yellow) = 20 marbles

2. Determine the number of purple marbles drawn:
There is 1 purple marble drawn.

3. Calculate the proportion of purple marbles:
[tex]\[ \text{Proportion of purple marbles} = \frac{\text{Number of purple marbles}}{\text{Total number of marbles}} = \frac{1}{20} \][/tex]

4. Convert the proportion to a percentage:
[tex]\[ \text{Percentage of purple marbles} = \left(\frac{1}{20}\right) \times 100\% = 5\% \][/tex]

Thus, the proportion of the marbles in the bag that Marcie would expect to be purple is [tex]\(5\%\)[/tex].

The correct answer is:
D. [tex]\(5\%\)[/tex]
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