Question

A bag contains 5 marbles that are each a different color. a marble is drawn, its color is recorded, and then the marble is placed back in the bag. this process is repeated until 30 marbles have been drawn. the table shows the results.

for which marble is the experimental probability of drawing the marble the same as the theoretical probability?

Answer 1

The marble for which the experimental probability is the same as the theoretical probability is the blue marble.

Step-by-step explanation:

The experimental probability of drawing a particular marble is determined by the number of times that marble is drawn. The theoretical probability of drawing a particular marble is determined by the total number of marbles in the bag. In the given scenario, we have 5 marbles, each of a different color, and a total of 30 draws. The marble for which the experimental probability is the same as the theoretical probability would be the one that is drawn the same number of times as the ratio of its quantity to the total number of marbles.

Let's look at the table to determine this:

Marble Color Number of Draws

Red 10

Blue 6

Green 5

Yellow 4

Orange 3

We can see that the marble drawn 6 times is the blue marble. Therefore, the experimental probability of drawing the blue marble is the same as the theoretical probability.

Answer 2

The experimental probability matches the theoretical probability for each marble since they are all equally likely to be drawn.

Step-by-step explanation:

In this scenario, with 5 marbles of different colors being drawn repeatedly with replacement until 30 marbles are drawn, the experimental probability of drawing any specific marble is the same as the theoretical probability for all the marbles. This is because, with replacement, the chances of drawing each marble remain constant at 1 out of 5, or 1/5. As the marbles are replaced after each draw, the probability of drawing a particular marble doesn't change throughout the process.

Therefore, for all the marbles in the bag, whether it's the first draw or the thirtieth, the experimental probability of drawing any particular marble will always align with the theoretical probability of 1/5.

Correct Answer: For each marble, the experimental probability matches the theoretical probability.