Westin performed an experiment in which he randomly pulled a marble from a bag, recorded its color, put it back, and then repeated the process. He did this

Question

36 times, and 9 of those times, he pulled a purple marble.
Which bags of marbles are good models for this experiment?
Select two that apply.
Responses

1 purple, 1 blue, 1 green, 1 red

4 purple, 5 blue, 2 green, 1 red

9 purple, 9 red, 9 green

4 purple, 4 blue, 4 yellow, 4 orange

Answer 1

To determine which bags of marbles would be good models for Westin's experiment, we need to analyze the proportion of purple marbles he observed during his trials.

Westin drew a purple marble 9 out of 36 times. To find the probability of drawing a purple marble in his experiment, we can calculate:

\[ \text{Proportion of purple marbles} = \frac{9}{36} = \frac{1}{4} = 0.25 \]

Now, let's check the given bags of marbles and see which ones have approximately the same proportion (0.25) of purple marbles:

1. 1 purple, 1 blue, 1 green, 1 red:

   • Total = 4 marbles
   • Purple proportion: \(\frac{1}{4} = 0.25\) (Good model)

2. 4 purple, 5 blue, 2 green, 1 red:

   • Total = 4 + 5 + 2 + 1 = 12 marbles
   • Purple proportion: \(\frac{4}{12} = \frac{1}{3} \approx 0.33\) (Not a good model)

3. 9 purple, 9 red, 9 green:

   • Total = 9 + 9 + 9 = 27 marbles
   • Purple proportion: \(\frac{9}{27} = \frac{1}{3} \approx 0.33\) (Not a good model)

4. 4 purple, 4 blue, 4 yellow, 4 orange:

   • Total = 4 + 4 + 4 + 4 = 16 marbles
   • Purple proportion: \(\frac{4}{16} = \frac{1}{4} = 0.25\) (Good model)

Based on this analysis, the bags that are good models for Westin's experiment are:

• 1 purple, 1 blue, 1 green, 1 red
• 4 purple, 4 blue, 4 yellow, 4 orange