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

Understanding the Context

Why This Data Set Matters Now—Trends and Cultural Relevance

In recent years, interest in probability and statistics has surged, driven by trends in data literacy, online education, and predictive tools in business and finance. The simplified marble model symbolizes how randomness influences outcomes—whether in stock movements, consumer behavior, or daily choices. This particular setup—few red marbles, no replacements—mirrors real-life scenarios where resources are limited and choices matter. As more people explore personal finance, coding basics, or critical thinking skills, understanding such probabilities offers practical value beyond the classroom.

This setup also aligns with a rising call for accessible, non-clickbait explanations that empower users to reason through chance—the kind of content charged on mobile devices, where quick yet thoughtful engagement drives meaningful dwell time.

Breaking Down the Probability: How to Calculate Drawing Two Red Marbles

Key Insights

The scenario begins with a bag containing 5 red, 4 blue, and 3 green marbles—totaling 12 marbles. When two marbles are drawn without replacement, the probability both are red depends on two linked events: the first draw, then the second, with numbers reduced.

Start with 5 red marbles out of 12 total. The chance the first marble is red is:

5 red out of 12 total →
5/12

After removing one red marble, only 4 red marbles remain and 11 total remain. The second draw now has:
4 red out of 11 total →
4/11

Multiplying these gives the combined probability:
(5/12) × (4/11) = 20/132 = 5/33

Final Thoughts

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