A box contains 4 red, 5 blue, and 6 green marbles. If two marbles are drawn at random without replacement, what is the probability both are green?
["Title: Probability Both Marbles Are Green: A Simple Calculation with Marbles", "Meta Description:\nLearn how to calculate the probability of drawing two green marbles without replacement from a box containing red, blue, and green marbles. Discover step-by-step math and real-world application.", "---", "When playing with marbles, challenging questions often arise about chance — like: What’s the probability of drawing two green marbles from a box with red, blue, and green marbles? In this guide, we break down the probability calculation clearly and simply.", "### The Problem\nA box contains:\n- 4 red marbles\n- 5 blue marbles\n- 6 green marbles", "If we randomly draw two marbles without replacement, what is the probability both marbles are green?", "---", "### Step 1: Total Number of Marbles\nFirst, find the total number of marbles in the box:\n[\n4 \ ext{ (red)} + 5 \ ext{ (blue)} + 6 \ ext{ (green)} = 15 \ ext{ marbles total}\n]", "---", "### Step 2: Probability of First Marble Being Green\nThe chance that the first marble drawn is green is the number of green marbles divided by the total marbles:\n[\nP(\ ext{first green}) = \frac{6}{15}\n]", "---", "### Step 3: Probability of Second Marble Being Green (Without Replacement)\nSince we do not replace the first marble, only 5 green marbles remain out of 14 total marbles:\n[\nP(\ ext{second green | first green}) = \frac{5}{14}\n]", "---", "### Step 4: Multiply Probabilities\nBecause the draws are dependent (without replacement), multiply the probabilities:\n[\nP(\ ext{both green}) = \frac{6}{15} \ imes \frac{5}{14}\n]", "Now calculate:\nFirst, simplify (\frac{6}{15}):\n[\n\frac{6}{15} = \frac{2}{5}\n]\nNow multiply:\n[\nP = \frac{2}{5} \ imes \frac{5}{14} = \frac{2 \ imes 5}{5 \ imes 14} = \frac{10}{70} = \frac{1}{7}\n]", "---", "### Final Answer\nThe probability that both marbles drawn are green is:\n[\n\frac{1}{7}\n]", "---", "### Summary\nWhen selecting two marbles without replacement from a box with 4 red, 5 blue, and 6 green marbles, the chance both are green is 1/7. This involves calculating sequential probabilities based on total and updated marble counts. Good fortune with your next marble draw!", "---", "Keywords: probability green marbles, draw marbles without replacement, probability calculator, marble probability, combinatorics probability, probability examples, math problem solution", "Also Search For: how to calculate probability two green marbles drawn, step-by-step probability formula, marble draw probability without replacement, probability of two green marbles, math problem probability green marbles."]
