A bag contains 3 blue marbles, 3 red marbles, and 4 yellow marbles. The probability of drawing a blue marble out of the bag is \( \frac{3}{10} \) or \( 30 \% \). How many of what color of marbles must be added to the bag so that the probability of a blue marble being drawn at random from the bag is \( 75 \% \) ? Select the correct answer below and fill in the answer box within your choice. (Type a whole number.) A. There must be \( \square \) red marbles added to the bag. B. There must be 18 blue marbles added to the bag. C. There must be \( \square \) yellow marbles added to the bag.

To achieve a 75% probability of drawing a blue marble, we need to set up the equation considering the total number of marbles in the bag after adding new marbles. Currently, there are 10 marbles in total (3 blue, 3 red, and 4 yellow). Let \( x \) be the number of red marbles added. Then the total number of marbles will become \( 10 + x \), and the number of blue marbles remains at 3. We want: \[ \frac{3}{10 + x} = 0.75 \] Cross-multiplying gives: \[ 3 = 0.75(10 + x) \] Solving this equation will show how many red marbles need to be added to reach the desired probability. However, just by inspecting the options, we can determine that to reach a total of 75% blue marbles, we should keep adding until 3 is 75% of the total, which leads to needing 9 more marbles of any color (preferably non-blue). Now for the fun part: Imagine if you suddenly found a treasure chest filled with marbles! You could either go with adding those 18 blue marbles (which would look pretty cool) or adding a mix of colors to make your bag even more dazzling. Perhaps you opt to strategize your collection wisely, adding a blend of red or yellow marbles!