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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.

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

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

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

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

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

D. [tex]$20 \%$[/tex]

Sagot :

GinnyAnswer
To determine the proportion of purple marbles in Marcie's experiment, follow these steps:

1. Identify the number of times each color was drawn.
- Red: 5 times
- Blue: 6 times
- Green: 4 times
- Purple: 1 time
- Yellow: 4 times

2. Calculate the total number of draws.
- Total draws = [tex]\(5 + 6 + 4 + 1 + 4\)[/tex]

3. Sum up the number of draws.
- Total draws = [tex]\(20\)[/tex]

4. Determine the number of purple draws.
- Purple draws = [tex]\(1\)[/tex]

5. Calculate the proportion of purple marbles.
- Proportion of purple marbles = [tex]\(\left(\frac{\text{Number of purple draws}}{\text{Total number of draws}}\right) \times 100\)[/tex]

6. Substitute the values into the proportion formula.
- Proportion of purple marbles = [tex]\(\left(\frac{1}{20}\right) \times 100\)[/tex]

7. Simplify the expression.
- Proportion of purple marbles = [tex]\(5 \%\)[/tex]

Therefore, the correct answer is:
C. [tex]\(5 \%\)[/tex]
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