Question
A spinner is divided into equal sections of pink, green, orange, white, blue and red. Eduardo spins the spinner 30 times and records the color it lands on. The table below shows his results.
Which of the following statements about the experimental and theoretical probabilities is accurate?
Responses
A The theoretical probability of the spinner landing on green is equal to the experimental probability.The theoretical probability of the spinner landing on green is equal to the experimental probability.
B The theoretical probability of the spinner landing on pink is less than the experimental probability.The theoretical probability of the spinner landing on pink is less than the experimental probability.
C The theoretical probability of the spinner landing on green is greater than the experimental probability.The theoretical probability of the spinner landing on green is greater than the experimental probability.
D The theoretical probability of the spinner landing on white is greater than the experimental probability.
Which of the following statements about the experimental and theoretical probabilities is accurate?
Responses
A The theoretical probability of the spinner landing on green is equal to the experimental probability.The theoretical probability of the spinner landing on green is equal to the experimental probability.
B The theoretical probability of the spinner landing on pink is less than the experimental probability.The theoretical probability of the spinner landing on pink is less than the experimental probability.
C The theoretical probability of the spinner landing on green is greater than the experimental probability.The theoretical probability of the spinner landing on green is greater than the experimental probability.
D The theoretical probability of the spinner landing on white is greater than the experimental probability.
Answers
Answered by
GPT-4o mini
To analyze the accuracy of the statements regarding the experimental and theoretical probabilities of the spinner, we first need to determine the theoretical probabilities and the experimental probabilities from Eduardo's results.
1. **Theoretical Probability**: Since the spinner is divided into equal sections, and it has 6 colors (pink, green, orange, white, blue, red), the theoretical probability for each color is:
\[
P(\text{any color}) = \frac{1}{6} \approx 0.1667
\]
2. **Experimental Probability**: To find the experimental probability, we need the number of times each color was recorded during the 30 spins. If you have Eduardo's exact results (the number of spins landing on each color), you can calculate the experimental probability for each color using:
\[
P(\text{color}) = \frac{\text{number of times the color appeared}}{\text{total spins}} = \frac{\text{count}}{30}
\]
Based on Eduardo's results, compare each experimental probability to the theoretical probabilities.
Now, let's evaluate the statements:
- **A**: "The theoretical probability of the spinner landing on green is equal to the experimental probability."
- **B**: "The theoretical probability of the spinner landing on pink is less than the experimental probability."
- **C**: "The theoretical probability of the spinner landing on green is greater than the experimental probability."
- **D**: "The theoretical probability of the spinner landing on white is greater than the experimental probability."
Without the exact numbers from Eduardo's results, I can't definitively determine which statement is accurate. However, when you analyze the data, you should compare the counts of each color from Eduardo's trials with the theoretical probability of \( \frac{1}{6} \) to see which statement holds true.
If you can provide the results from Eduardo's experiment, I would be able to give a specific answer regarding which statement is accurate.
1. **Theoretical Probability**: Since the spinner is divided into equal sections, and it has 6 colors (pink, green, orange, white, blue, red), the theoretical probability for each color is:
\[
P(\text{any color}) = \frac{1}{6} \approx 0.1667
\]
2. **Experimental Probability**: To find the experimental probability, we need the number of times each color was recorded during the 30 spins. If you have Eduardo's exact results (the number of spins landing on each color), you can calculate the experimental probability for each color using:
\[
P(\text{color}) = \frac{\text{number of times the color appeared}}{\text{total spins}} = \frac{\text{count}}{30}
\]
Based on Eduardo's results, compare each experimental probability to the theoretical probabilities.
Now, let's evaluate the statements:
- **A**: "The theoretical probability of the spinner landing on green is equal to the experimental probability."
- **B**: "The theoretical probability of the spinner landing on pink is less than the experimental probability."
- **C**: "The theoretical probability of the spinner landing on green is greater than the experimental probability."
- **D**: "The theoretical probability of the spinner landing on white is greater than the experimental probability."
Without the exact numbers from Eduardo's results, I can't definitively determine which statement is accurate. However, when you analyze the data, you should compare the counts of each color from Eduardo's trials with the theoretical probability of \( \frac{1}{6} \) to see which statement holds true.
If you can provide the results from Eduardo's experiment, I would be able to give a specific answer regarding which statement is accurate.