A bag of marbles contains 6 purple, 9 green, and 3 pink marbles. Paulina performed an experiment in which she randomly pulled a marble from the bag, recorded its colour, put it back, and then repeated. The following table represents the number of times each color of marble was pulled.

Question

Color
Frequency
Purple
15
Green
15
Pink
6


Compare the experimental probabilities to the expected probabilities.
Match each color on the left with the correct description on the right.

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Purple
The experimental probability is greater than the expected probability.
Green
The experimental probability is the same as the expected probability.
Pink
The experimental probability is less than the expected probability.

Answer 1

To compare the experimental and expected probabilities for each marble color, we first need to determine the expected probabilities based on the total number of marbles.

Total number of marbles:

• Purple: 6
• Green: 9
• Pink: 3

Total = 6 + 9 + 3 = 18 marbles.

Expected probabilities:

• Expected probability of pulling a purple marble: \( \frac{6}{18} = \frac{1}{3} \approx 0.33 \)
• Expected probability of pulling a green marble: \( \frac{9}{18} = \frac{1}{2} = 0.5 \)
• Expected probability of pulling a pink marble: \( \frac{3}{18} = \frac{1}{6} \approx 0.17 \)

Experimental probabilities from the experiment:

• Total pulls = 15 (purple) + 15 (green) + 6 (pink) = 36 pulls.

• Experimental probability of pulling a purple marble: \( \frac{15}{36} = \frac{5}{12} \approx 0.42 \)

• Experimental probability of pulling a green marble: \( \frac{15}{36} = \frac{5}{12} \approx 0.42 \)

• Experimental probability of pulling a pink marble: \( \frac{6}{36} = \frac{1}{6} \approx 0.17 \)

Now we will compare the experimental probabilities to the expected probabilities.

1. Purple:

   • Experimental probability: \( \frac{5}{12} \approx 0.42 \)
   • Expected probability: \( \frac{1}{3} \approx 0.33 \)
   • The experimental probability is greater than the expected probability.

2. Green:

   • Experimental probability: \( \frac{5}{12} \approx 0.42 \)
   • Expected probability: \( \frac{1}{2} = 0.5 \)
   • The experimental probability is less than the expected probability.

3. Pink:

   • Experimental probability: \( \frac{1}{6} \approx 0.17 \)
   • Expected probability: \( \frac{1}{6} \approx 0.17 \)
   • The experimental probability is the same as the expected probability.

Final matching:

• Purple: The experimental probability is greater than the expected probability.
• Green: The experimental probability is less than the expected probability.
• Pink: The experimental probability is the same as the expected probability.