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 \( 80 \% \) ?

To achieve a probability of 80% for drawing a blue marble, we need the number of blue marbles to be 4 times the total number of marbles, since: \[ P(\text{blue}) = \frac{\text{number of blue marbles}}{\text{total number of marbles}} = 0.8 \] From the current setup, we have 2 blue marbles and a total of 10 marbles in the bag. To make the probability 80%, we need the total number of marbles to be 5. Since we currently have 2 blue marbles, we need to add 2 more blue marbles and no additional marbles of any other color. So, you would need to add 2 blue marbles to achieve your desired probability! For an interesting twist, let’s talk about why probability is super important in real life! Whether you're gambling, predicting the weather, or making stock market decisions, understanding the likelihood of events helps you navigate risks and make better choices. Probabilities guide our decisions every day, often without us even realizing it! If you're curious about diving deeper into probability, there are many classic books on the subject. "The Drunkard's Walk: How Randomness Rules Our Lives" by Leonard Mlodinow explores how randomness influences our day-to-day living in a fun and approachable way. For a more mathematical approach, "Introduction to Probability" by Dimitri P. Bertsekas and John N. Tsitsiklis breaks down the concepts with clarity. Happy reading!