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Layer 3: 3 choices - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 A soil scientist uses spectroscopy to classify soil types across 200 plots: 30% sandy, 50% loamy, 20% clay. She samples 5 plots from each type. If she runs a chemical analysis on each, what is the minimum number of samples that must be high-clay to ensure at least 3 samples are from high-clay plots, assuming worst-case random placement?

📌 Worst case: maximize non-clay samples first.

📌 Total high-clay plots: 20% of 200 = 40, but only 5 can be sampled per type. Sample 5 sandy, 5 loamy, 5 clay → 15 samples, none high-clay.

📌 To guarantee 3 high-clay, assume worst: 5 each from sandy and loamy (0 high-clay), and only from clay: up to 5 high-clay available.

📌 To ensure 3 high-clay samples, need 3 from clay. But worst case, you pick from other types first.

📌 Max non-high-clay samples that could be picked: 5 (sandy) + 5 (loamy) + 5 (clay sample) = 15 — none high-clay.

📌 But to *ensure* 3 high-clay, consider: if you pick 5+5+5 = 15 samples, all non-high-clay possible.

📌 So you need 3 more high-clay samples, but only 5 available. The next 3 samples after 15 may be high-clay, but worst-case you pick non-clay until exhausted.

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