Question
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
a. the theoretical probability of selecting a red marker is __ than the experimental probability
b. the theoretical probability of selecting a blue marker is __ than the experimental probability
c. the theoretical probability of selecting a purple marker is __ than the experimental probability
color | frequency
red : 9
blue : 11
purple : 10
a. the theoretical probability of selecting a red marker is __ than the experimental probability
b. the theoretical probability of selecting a blue marker is __ than the experimental probability
c. the theoretical probability of selecting a purple marker is __ than the experimental probability
color | frequency
red : 9
blue : 11
purple : 10
Answers
GPT-4o mini
To determine the theoretical and experimental probabilities, we need to calculate these probabilities based on the total number of selections and then compare them.
### Step 1: Calculate the Total Frequency
Total frequency = Frequency of Red + Frequency of Blue + Frequency of Purple
= 9 (red) + 11 (blue) + 10 (purple)
= 30
### Step 2: Calculate the Theoretical Probability
Since Harish is choosing colors at random, we assume that the probability of selecting each color is equal. Given three colors (red, blue, purple), the theoretical probability for each color is:
- Theoretical Probability of Red = 1/3 ≈ 0.33
- Theoretical Probability of Blue = 1/3 ≈ 0.33
- Theoretical Probability of Purple = 1/3 ≈ 0.33
### Step 3: Calculate the Experimental Probability
Experimental probability is calculated based on the number of times each color was selected divided by the total selections.
- Experimental Probability of Red = Frequency of Red / Total Frequency = 9/30 = 0.30
- Experimental Probability of Blue = Frequency of Blue / Total Frequency = 11/30 ≈ 0.37
- Experimental Probability of Purple = Frequency of Purple / Total Frequency = 10/30 ≈ 0.33
### Step 4: Compare Theoretical and Experimental Probabilities
a. The theoretical probability of selecting a **red marker** is **greater** than the experimental probability (0.33 vs 0.30).
b. The theoretical probability of selecting a **blue marker** is **less** than the experimental probability (0.33 vs 0.37).
c. The theoretical probability of selecting a **purple marker** is **equal to** the experimental probability (0.33 vs 0.33).
So the answers are:
a. The theoretical probability of selecting a red marker is **greater** than the experimental probability.
b. The theoretical probability of selecting a blue marker is **less** than the experimental probability.
c. The theoretical probability of selecting a purple marker is **equal to** the experimental probability.
### Step 1: Calculate the Total Frequency
Total frequency = Frequency of Red + Frequency of Blue + Frequency of Purple
= 9 (red) + 11 (blue) + 10 (purple)
= 30
### Step 2: Calculate the Theoretical Probability
Since Harish is choosing colors at random, we assume that the probability of selecting each color is equal. Given three colors (red, blue, purple), the theoretical probability for each color is:
- Theoretical Probability of Red = 1/3 ≈ 0.33
- Theoretical Probability of Blue = 1/3 ≈ 0.33
- Theoretical Probability of Purple = 1/3 ≈ 0.33
### Step 3: Calculate the Experimental Probability
Experimental probability is calculated based on the number of times each color was selected divided by the total selections.
- Experimental Probability of Red = Frequency of Red / Total Frequency = 9/30 = 0.30
- Experimental Probability of Blue = Frequency of Blue / Total Frequency = 11/30 ≈ 0.37
- Experimental Probability of Purple = Frequency of Purple / Total Frequency = 10/30 ≈ 0.33
### Step 4: Compare Theoretical and Experimental Probabilities
a. The theoretical probability of selecting a **red marker** is **greater** than the experimental probability (0.33 vs 0.30).
b. The theoretical probability of selecting a **blue marker** is **less** than the experimental probability (0.33 vs 0.37).
c. The theoretical probability of selecting a **purple marker** is **equal to** the experimental probability (0.33 vs 0.33).
So the answers are:
a. The theoretical probability of selecting a red marker is **greater** than the experimental probability.
b. The theoretical probability of selecting a blue marker is **less** than the experimental probability.
c. The theoretical probability of selecting a purple marker is **equal to** the experimental probability.