Harish is completing an art project by choosing colors at random to fill in different pieces of the project. He has a red marker, a blue marker, and a purple marker. He records how many times he selects each marker and displays the results in a table.

Question

Color Frequency
Red 9
Blue 11
Purple 10
Fill in the blanks to complete the sentences comparing the experimental and theoretical probabilities.
The theoretical probability of selecting a red marker is
than the experimental probability.

The theoretical probability of selecting a blue marker is
than the experimental probability.

The theoretical probability of selecting a purple marker is
than the experimental probability.

Answer 1

To determine the theoretical and experimental probabilities, we first need to calculate both.

1. Total selections:

   • Red: 9
   • Blue: 11
   • Purple: 10

   Total = 9 + 11 + 10 = 30 selections

2. Theoretical probabilities: Assuming each color has an equal chance of being selected, the theoretical probabilities for each color, considering that there are three colors, are:

• Theoretical probability of Red = 1/3
• Theoretical probability of Blue = 1/3
• Theoretical probability of Purple = 1/3

3. Experimental probabilities:
   • Experimental probability of Red = Frequency of Red / Total selections = 9/30 = 0.3
   • Experimental probability of Blue = Frequency of Blue / Total selections = 11/30 ≈ 0.3667
   • Experimental probability of Purple = Frequency of Purple / Total selections = 10/30 ≈ 0.3333

Now, let's compare the theoretical and experimental probabilities:

1. Red:

   • Theoretical Probability = 1/3 ≈ 0.3333
   • Experimental Probability = 9/30 = 0.3
   • So, the theoretical probability of selecting a red marker is greater than the experimental probability.

2. Blue:

   • Theoretical Probability = 1/3 ≈ 0.3333
   • Experimental Probability = 11/30 ≈ 0.3667
   • So, the theoretical probability of selecting a blue marker is less than the experimental probability.

3. Purple:

   • Theoretical Probability = 1/3 ≈ 0.3333
   • Experimental Probability = 10/30 ≈ 0.3333
   • So, the theoretical probability of selecting a purple marker is equal to the experimental probability.

Now we can fill in the blanks:

• The theoretical probability of selecting a red marker is greater than the experimental probability.
• The theoretical probability of selecting a blue marker is less than the experimental probability.
• The theoretical probability of selecting a purple marker is equal to the experimental probability.