Jayden did an experiment in which he pulled a marble from a bag, recorded its color, put it back, and then repeated the process. He did this 18 times, and 6 of those times, he pulled a yellow marble.

Question

Which bags of marbles are good models for this experiment?
Select two that apply.
Responses

4 purple, 5 blue, 2 yellow

6 purple, 2 blue, 4 yellow

4 orange, 6 red, 5 yellow

6 purple, 9 yellow

6 purple, 6 blue, 6 green, 6 yellow

Answer 1

To determine which bags of marbles are good models for Jayden's experiment, we need to analyze the proportion of yellow marbles in each bag relative to the total number of marbles.

In Jayden's experiment, he pulled a yellow marble 6 out of 18 times, which gives a probability of pulling a yellow marble as:

\[ \text{Probability of yellow marble} = \frac{6}{18} = \frac{1}{3} \]

Now, we will evaluate each of the bags provided:

1. 4 purple, 5 blue, 2 yellow:

   • Total = 4 + 5 + 2 = 11
   • Probability of yellow = \(\frac{2}{11}\) (not close to \(\frac{1}{3}\))

2. 6 purple, 2 blue, 4 yellow:

   • Total = 6 + 2 + 4 = 12
   • Probability of yellow = \(\frac{4}{12} = \frac{1}{3}\) (matches with Jayden's experiment)

3. 4 orange, 6 red, 5 yellow:

   • Total = 4 + 6 + 5 = 15
   • Probability of yellow = \(\frac{5}{15} = \frac{1}{3}\) (matches with Jayden's experiment)

4. 6 purple, 9 yellow:

   • Total = 6 + 9 = 15
   • Probability of yellow = \(\frac{9}{15} = \frac{3}{5}\) (not close to \(\frac{1}{3}\))

5. 6 purple, 6 blue, 6 green, 6 yellow:

   • Total = 6 + 6 + 6 + 6 = 24
   • Probability of yellow = \(\frac{6}{24} = \frac{1}{4}\) (not close to \(\frac{1}{3}\))

Based on this analysis, the two bags that are good models for the experiment are:

• 6 purple, 2 blue, 4 yellow
• 4 orange, 6 red, 5 yellow