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.
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.
Answers
GPT-4o mini
To find the theoretical probability of picking a blue marble from the bag, we start by determining the total number of marbles.
The bag contains:
- 1 blue marble
- 1 yellow marble
- 2 green marbles
Total number of marbles = 1 (blue) + 1 (yellow) + 2 (green) = 4 marbles.
Now, the theoretical probability of picking a blue marble is:
\[
P(B) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{1}{4} = \frac{25}{100}
\]
Next, we calculate the experimental probability based on the results of the 100 spins:
\[
\text{Experimental probability of blue} = \frac{\text{Number of times blue was picked}}{\text{Total spins}} = \frac{30}{100}
\]
Now, we compare the experimental probability to the theoretical probability:
- Experimental probability of blue = \( \frac{30}{100} \)
- Theoretical probability of blue = \( \frac{25}{100} \)
Thus, we can conclude:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**
So the correct response is:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**
The bag contains:
- 1 blue marble
- 1 yellow marble
- 2 green marbles
Total number of marbles = 1 (blue) + 1 (yellow) + 2 (green) = 4 marbles.
Now, the theoretical probability of picking a blue marble is:
\[
P(B) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{1}{4} = \frac{25}{100}
\]
Next, we calculate the experimental probability based on the results of the 100 spins:
\[
\text{Experimental probability of blue} = \frac{\text{Number of times blue was picked}}{\text{Total spins}} = \frac{30}{100}
\]
Now, we compare the experimental probability to the theoretical probability:
- Experimental probability of blue = \( \frac{30}{100} \)
- Theoretical probability of blue = \( \frac{25}{100} \)
Thus, we can conclude:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**
So the correct response is:
**The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.**