Question: A bag contains 5 yellow chips, 7 purple chips, and 3 orange chips. If three chips are drawn at random without replacement, what is the probability that all three are of different colors?

Mon, 04 May 2026 17:59:51 +0000

**Why Users Are Exploring the Chips Probability Puzzle**
In today’s fast-paced digital landscape, even simple math problems can spark quiet curiosity—especially when tied to tangible, familiar scenarios. The question, *A bag contains 5 yellow chips, 7 purple chips, and 3 orange chips. If three chips are drawn at random without replacement, what is the probability that all three are of different colors?* fits this niche perfectly. It blends everyday intuition with statistical insight, making it a natural curiosity for users exploring probability in real-world contexts. With mobile search spikes around games, puzzles, and learning tools, this question reflects growing intent among US audiences searching for clear, factual explanations behind everyday odds. **Understanding the Question and Its Hidden Insight**
The scenario involves drawing three chips without replacement from a bag with distinct quantities: yellow (5), purple (7), and orange (3). The challenge lies in calculating the exact probability that each chip draws a unique color—a task that invites both curiosity and practical calculation. This isn’t just abstract math; it’s a gateway to understanding how probability shapes decision-making in games, risk analysis, or even data interpretation. Users drawn to such questions often seek a clear, step-by-step path to grasp complex sugar-coated concepts—nowhere more than in SEO-driven content where clarity builds trust. **How to Calculate the Likelihood Safely and Clearly**
To solve this, start with total possibilities: total chips = 5 + 7 + 3 = 15. The total ways to pick any 3 chips from 15 is given by the combination formula C(15,3) = 455. Now, calculate the favorable outcomes—those where each chip is a different color. We need one yellow, one purple, and one orange. The number of such combinations is 5 × 7 × 3 = 105. Since order doesn’t matter in a draw, divide combinations accordingly, but here direct multiplication suffices for total favorable, since only one of each color is selected. Thus, the probability is 105 ÷ 455, simplifying to 21/91 or 3/13—roughly 23.2%. This precise breakdown, presented simply, invites deep engagement and long scroll time. **Common Queries: What People