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.

1 answer

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.