Question
A bag of marbles has one blue, one yellow, and two green marbles.
If you spin a fair spinner (like the one shown below) to simulate picking a marble randomly from the bag and replacing it, you get the following results after 100 times.
Blue (B) = 30 times
Yellow (Y) = 27 times
Green (G) = 43 times
Compare the experimental probability after spinning it 100 times to the theoretical probability of picking a blue marble.
(2 points)
Responses
The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.
The experimental probability is 30/100 , which is greater than the theoretical probability of 25/100 .
The experimental probability is 27/100, which is greater than the theoretical probability of 25/100.
The experimental probability is 27/100 , which is greater than the theoretical probability of 25/100 .
The experimental probability is 25/100, which is less than the theoretical probability of 30/100.
The experimental probability is 25/100 , which is less than the theoretical probability of 30/100 .
The experimental probability is 27/100, which is less than the theoretical probability of 30/100.
The experimental probability is 27/100 , which is less than the theoretical probability of 30/100 .
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If you spin a fair spinner (like the one shown below) to simulate picking a marble randomly from the bag and replacing it, you get the following results after 100 times.
Blue (B) = 30 times
Yellow (Y) = 27 times
Green (G) = 43 times
Compare the experimental probability after spinning it 100 times to the theoretical probability of picking a blue marble.
(2 points)
Responses
The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.
The experimental probability is 30/100 , which is greater than the theoretical probability of 25/100 .
The experimental probability is 27/100, which is greater than the theoretical probability of 25/100.
The experimental probability is 27/100 , which is greater than the theoretical probability of 25/100 .
The experimental probability is 25/100, which is less than the theoretical probability of 30/100.
The experimental probability is 25/100 , which is less than the theoretical probability of 30/100 .
The experimental probability is 27/100, which is less than the theoretical probability of 30/100.
The experimental probability is 27/100 , which is less than the theoretical probability of 30/100 .
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Answers
GPT-4o mini
To compare the experimental probability to the theoretical probability of picking a blue marble:
1. **Theoretical Probability**:
- There are 4 marbles in total: 1 blue, 1 yellow, and 2 green.
- The probability of picking a blue marble theoretically is:
\[
P(B) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{1}{4} = \frac{25}{100}.
\]
2. **Experimental Probability**:
- From the results of spinning the spinner 100 times, the blue marble was picked 30 times.
- The experimental probability of picking a blue marble is:
\[
P(B) = \frac{\text{Number of times blue was picked}}{\text{Total spins}} = \frac{30}{100}.
\]
Comparing the two probabilities:
- **Experimental Probability** = \( \frac{30}{100} \)
- **Theoretical Probability** = \( \frac{25}{100} \)
Thus, the experimental probability (30/100) is greater than the theoretical probability (25/100).
The correct response would be:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**
1. **Theoretical Probability**:
- There are 4 marbles in total: 1 blue, 1 yellow, and 2 green.
- The probability of picking a blue marble theoretically is:
\[
P(B) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{1}{4} = \frac{25}{100}.
\]
2. **Experimental Probability**:
- From the results of spinning the spinner 100 times, the blue marble was picked 30 times.
- The experimental probability of picking a blue marble is:
\[
P(B) = \frac{\text{Number of times blue was picked}}{\text{Total spins}} = \frac{30}{100}.
\]
Comparing the two probabilities:
- **Experimental Probability** = \( \frac{30}{100} \)
- **Theoretical Probability** = \( \frac{25}{100} \)
Thus, the experimental probability (30/100) is greater than the theoretical probability (25/100).
The correct response would be:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**