A bag contains 2 blue marbles, 6 red marbles, and 2 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 \( 90 \% \) ? 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 \( \square \) red marbles added to the bag. C. There must be \( \square \) blue marbles added to the bag.

To make the probability of drawing a blue marble \( 90\% \), we can set up the equation based on the total number of marbles. There are currently \( 2 + 6 + 2 = 10 \) marbles in total. Let \( x \) be the number of blue marbles added. The new total number of marbles will be \( 10 + x \), and the number of blue marbles will be \( 2 + x \). Setting up the equation for the probability: \[ \frac{2 + x}{10 + x} = 0.9 \] Cross-multiplying, we get: \[ 2 + x = 0.9(10 + x) \] This simplifies to: \[ 2 + x = 9 + 0.9x \] Rearranging terms brings us to: \[ 2 - 9 = 0.9x - x \] \[ -7 = -0.1x \implies x = 70 \] Thus, the correct answer is C. There must be \( 70 \) blue marbles added to the bag. But wait! Here’s a fun fact: Did you know that the concept of probability dates back to the 16th century with mathematicians like Gerolamo Cardano? He famously explored the mathematics of games of chance! And did you know there’s a famous gambler’s fallacy? Some people believe if a particular outcome occurs multiple times in a row (like drawing only red marbles), it’s less likely to happen again soon when in reality, each draw is independent. So don't let superstition influence your calculations!