A bag contains 5 red, 4 blue, and 6 green marbles. Two marbles are drawn at random without replacement. Find the probability both are green.
["Discover: The Unexpected Math Behind a Simple Marble Game—And Why It Still Matters", "Have you ever paused while watching a game of chance unfold, wondering how much suspense magical randomness really adds? Today, we’re diving into a classic probability problem that blends simplicity with insight: What is the chance that two marbles drawn from a bag containing 5 red, 4 blue, and 6 green marbles are both green—drawn without replacement?", "This isn’t just a math exercise; it’s a gateway into understanding unpredictable systems, which influence everything from games of chance to financial risk and strategy. The setup is straightforward: a bag holds 15 marbles total—5 red, 4 blue, and 6 green. Two marbles are drawn randomly, one after the other, with no replacement. The goal: uncover the true probability both are green, and why this question continues to spark curiosity in a digital world hungry for clarity.", "Why This Marble Setup Is Rise-Ready in the US", "Marble draw probability puzzles like this are more than classroom questions—they reflect real-life patterns of chance and uncertainty. In the US, interest in randomness, strategy, and decision-making is growing, especially as people seek logical frameworks in unpredictable environments. From backyard games and classroom learning to online simulations and educational content, the fascination with outcomes shaped by chance remains strong.", "The simplicity of the marble scenario makes it a perfect fit for mobile-first consumers searching for quick, digestible insights. It fits the Discover ecosystem’s demand for content that informs without overwhelm—ideal for sparking interest across casual users and lifelong learners alike.", "Understanding the Setup, Step-by-Step", "To calculate the probability both drawn marbles are green, begin with clarity. The bag contains 5 red, 4 blue, and 6 green marbles—totaling 15. Since marbles are drawn without replacement, the first draw affects the second.", "- Probability the first marble is green: 6 out of 15 \n- After one green marble is removed, 5 green remain out of 14 total", "The joint probability is the product: \n\[\n\frac{6}{15} \ imes \frac{5}{14} = \frac{30}{210} = \frac{1}{7} \approx 0.1429\n\]", "That means there’s about a 14.3% chance both marbles are green—an"]
