A box contains 3 red, 4 blue, and 5 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?

Sat, 02 May 2026 18:15:42 +0000

**A box contains 3 red, 4 blue, and 5 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are blue?** In everyday curiosity surrounding chance and probability, a simple exercise like drawing marbles often sparks interest—especially when framed as a real-world puzzle with tangible examples. The scenario involves a box containing three red, four blue, and five green marbles—totaling 12 marbles—and the question centers on drawing two without replacement. This setup invites a deeper look into basic probability—a concept increasingly relevant in a data-driven culture where understanding randomness helps inform decisions. Real-world curiosity about patterns and likelihoods fuels engagement with such problems. In the U.S., this type of math joins broader interest in statistics, games, and logical reasoning—mentioned in everything from home experiments to finance education. People increasingly seek clarity in decision-making, whether analyzing risk or understanding random chance. This demand places probability puzzles like this firmly within a growing digital footprint. The setup remains neutral and factual: a box with 3 red, 4 blue, and 5 green marbles—exactly as described—faces the chance of yielding two blue marbles drawn sequentially without replacement. Probability calculations grounded in this distribution reveal insightful patterns without complexity. The exact chance—triggering focus and mental engagement—relies on combination math: choosing 2 blue marbles from 4, divided by choosing any 2 from 12.