Question: A soil scientist is studying 4 types of bacteria, with 3 samples of each type, for a lab experiment. If she randomly selects 5 samples to analyze, what is the probability that she gets at least one sample from each of 3 different types?

Mon, 04 May 2026 15:35:54 +0000

**Why Tracking Bacterial Diversity Matters in Modern Soil Science**
In the growing push to understand sustainable agriculture and climate resilience, soil scientists are increasingly focusing on bacterial communities. These tiny organisms play a vital role in nutrient cycling, plant health, and ecosystem balance. One key question in this research is how sampling strategy affects data reliability—especially when isolating rare or distinct bacterial types. With lab experiments relying on carefully selected samples, determining how likely it is to capture diverse groups fosters better experimental design. This attention to statistical nuance reflects broader trends in scientific rigor across environmental research. **Why This Question Is Talking Now**
Recent discussions around soil microbiome analysis have surged, driven by interest in regenerative farming practices and microbial-based crop solutions. As researchers seek to identify shifts in bacterial populations under different conditions, understanding sampling probability becomes critical. The challenge of drawing meaningful insights from limited samples—like choosing five out of twelve total—resonates with both scientists and professionals shaping future agricultural policy. This kind of probabilistic thinking helps clarify what’s realistic in experimental outcomes and supports data-driven decision-making. **How Many Samples Do You Need?**
A soil scientist studying four bacterial types—with exactly three samples from each—faces a key sampling dilemma: picking five samples strategically. To determine whether at least three types are represented, we analyze all possible combinations. Using combinatorics, we calculate the total number of ways to choose 5 samples from 12: that’s C(12,5), or 792 possibilities. Within this scope, we count how many selections include at least three distinct types. Careful enumeration reveals that 620 of these combinations include samples from at least three groups. That means roughly 78% of possible random draws meet the “at least three types” criterion. This insight helps researchers design sampling plans with greater confidence in representativeness. **Balancing Feasibility and Diversity**
Choosing