Wed, 29 Apr 2026 21:08:27 +0000

A bag contains 4 red, 5 blue, and 6 green marbles. If two marbles are drawn at random, what is the probability that both are green? This question, while deceptively simple, taps into broader curiosity about chance and probability—a topic gaining steady interest across educational and casual audiences in the US. With growing engagement in data literacy, financial literacy, and analytical thinking, this type of probability problem stands out as both approachable and intellectually satisfying. Though the scenario is fictional, the mathematical principles apply directly to real-world decision-making scenarios involving selection, risk, and expected outcomes. ### Understanding the Probability Behind the Marble Draw To calculate the probability that both drawn marbles are green, begin with the total number of marbles in the bag: 4 red + 5 blue + 6 green = 15 marbles total. Drawing two marbles at random means considering combinations—how many unique pairs can be formed. The total number of ways to choose 2 marbles from 15 is given by the combination formula C(15, 2), which equals 105 distinct pairs. Only the combinations where both marbles are green contribute to the desired outcome. With 6 green marbles, the number of ways to pick 2 green marbles is C(6, 2) = 15. This gives a basic probability of 15/105, which simplifies to 1/7—about 14.3%. Understanding this step-by-step breakdown builds clarity and trust, essential for spreading accurate knowledge. ### Why This Question Frequently Appears Online