A game has a bag of marbles which you must choose from. The bag has the following colors: 1 black marble, 3 green marbles, 3 red marbles, 1 yellow, and 2 blue marbles. If the marbles are placed back into the bag, what is the sample space if I choose a marble, replace it, and then choose another marble?

When you choose a marble from the bag and then replace it, you have a combination of colors for each of your selections. Since there are 10 total marbles (1 black, 3 green, 3 red, 1 yellow, and 2 blue), you can represent the sample space for two selections as pairs of colors. The sample space consists of all possible pairs of colors (e.g., (black, green), (green, red), etc.), resulting in \(10 \times 10 = 100\) different combinations. So, your sample space is made up of pairs like (B, G), (G, R), (Y, B), and so on! To have some fun with your choices, think of the marbles as characters in a story! For example, the black marble could be a mysterious hero, the green marbles might represent a trio of playful fairies, while the red marbles are thrilling adventurers. Each pair you draw can weave together mini-stories based on the colors you get, making your marble-picking adventures both educational and entertaining!