Answered

Select the correct answer.

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



Answer :

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

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

2. Find the total number of draws:
Add the number of times each color was drawn to get the total:
[tex]\[ 5 (\text{red}) + 6 (\text{blue}) + 4 (\text{green}) + 1 (\text{purple}) + 4 (\text{yellow}) = 20 \text{ draws} \][/tex]

3. Calculate the proportion of purple marbles:
- The number of times purple marble was drawn = 1
- Total number of draws = 20

The proportion of purple marbles is calculated as follows:
[tex]\[ \frac{\text{Number of times purple was drawn}}{\text{Total number of draws}} \times 100 = \frac{1}{20} \times 100 = 5\% \][/tex]

Therefore, the proportion of the marbles in the bag that Marcie would expect to be purple is:
[tex]\[ \boxed{5\%} \][/tex]
So the correct answer is:
D. [tex]$5\%$[/tex]