Question

There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..

Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11


Compare the theoretical probability and experimental probability of pulling a green marble from the bag.

A The theoretical probability, P(green), is 50%, and the experimental probability is 11.5%.
B The theoretical probability, P(green), is 25%, and the experimental probability is 25%.
C The theoretical probability, P(green), is 25%, and the experimental probability is 17.5%.
D The theoretical probability, P(green), is 50%, and the experimental probability is 7.0%.

Answer 1

Explanation:

To compare the theoretical probability and experimental probability of pulling a green marble, we need to calculate both probabilities.

The theoretical probability can be calculated by dividing the number of green marbles by the total number of marbles in the bag:

Theoretical probability of pulling a green marble (P(green)) = (number of green marbles) / (total number of marbles)

In this case, the number of green marbles is 10, and the total number of marbles is 10 + 10 + 10 + 10 = 40.

P(green) = 10 / 40 = 1/4 = 25%

Now let's calculate the experimental probability. The experimental probability is determined by the frequency of pulling a green marble in the given trials:

Experimental probability of pulling a green marble = (frequency of green marble) / (total number of trials)

From the table, we see that the frequency of pulling a green marble is 7, and the total number of trials is 40.

Experimental probability = 7 / 40 = 0.175 = 17.5%

Comparing the theoretical and experimental probabilities, we find that the correct answer is:

C) The theoretical probability, P(green), is 25%, and the experimental probability is 17.5%.