To determine the correct response, we need to calculate both the experimental probability and the theoretical probability of picking a blue marble from the bag.
Theoretical Probability:
- The bag contains:
- 1 blue marble
- 1 yellow marble
- 2 green marbles
Total marbles = 1 + 1 + 2 = 4
The theoretical probability of picking a blue marble (B) is given by the formula:
\[ P(B) = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{1}{4} = \frac{25}{100} \]
Experimental Probability: From the spinner results after 100 spins:
- Blue (B) = 30 times
The experimental probability of picking a blue marble is calculated as follows:
\[ P(B)_{\text{experimental}} = \frac{\text{Number of times blue was spun}}{\text{Total spins}} = \frac{30}{100} \]
Comparison:
- The experimental probability is \( \frac{30}{100} \).
- The theoretical probability is \( \frac{25}{100} \).
Now we can compare these probabilities:
- \( \frac{30}{100} \) (experimental) is greater than \( \frac{25}{100} \) (theoretical).
Thus, the correct response is:
The experimental probability is 30/100, which is greater than the theoretical probability of 25/100.