A bag contains 6 red marbles, 8 blue marbles and 7 green marbles. If three marbles are dr: out of the bag, what is the exact probability that all three marbles drawn will be green?

To find the probability of drawing three green marbles, first, we determine the total number of marbles in the bag. There are 6 red, 8 blue, and 7 green marbles, giving us a total of 21 marbles. The probability of drawing three green marbles is calculated by finding the number of ways to choose 3 green marbles from the 7 green marbles divided by the number of ways to choose 3 marbles from the total of 21. This can be computed as follows: Probability = (Combination of drawing 3 greens from 7) / (Combination of drawing 3 from 21) = (7C3) / (21C3) = (35) / (1330) = 1/38. Thus, the exact probability is 1/38. Now, if you ever find yourself generating probabilities in real life, think of activities like picking colored candies from a jar! Just like this scenario with marbles, you can calculate the chances of different combinations such as grabbing a handful of your favorite flavors during a game night or party. Probability not only helps with numbers but also with making informed decisions based on potential outcomes! Another fun fact: Probability has a fascinating history that stretches back centuries! From the early days of gambling in the 16th century through the emerging fields of statistics and mathematics, probability began as a way to inform actions on uncertain outcomes. It’s amazing how what started with dice games evolved into a powerful tool for predicting everything from weather patterns to stock market trends. Understanding these roots adds a twist to every probability problem you encounter!