A bag contains 2 blue marbles, 4 red marbles, and 4 yellow marbles. The probability of drawing a blue marble out of the bag is \( \frac{2}{10} \) or \( 20 \% \). 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 \( 80 \% \) ? Select the correct answer below and fill in the answer box within your choice. (Type a whole number.) A. There must be \( \square \) yellow marbles added to the bag. B. There must be \( \square \) blue marbles added to the bag. C. There must be \( \square \) red marbles added to the bag.

To achieve an 80% probability for blue marbles, we need a new total amount of marbles in the bag where blue marbles represent 80% of them. Let's assume we add \( x \) blue marbles. Initially, there are 10 marbles (2 blue, 4 red, 4 yellow). So, after adding, the total number of marbles becomes \( 10 + x \). For blue marbles to be 80% of this total: \[ \frac{2 + x}{10 + x} = 0.8 \] By solving the equation: \[ 2 + x = 0.8(10 + x) \] \[ 2 + x = 8 + 0.8x \] \[ 2 + x - 0.8x = 8 \] \[ 0.2x = 6 \] \[ x = 30 \] Therefore, you must add **30 blue marbles** to achieve an 80% probability. B. There must be \( 30 \) blue marbles added to the bag.