Question: An ichthyologist studies fish in a pond with 10 species, 4 of which are migratory. If she randomly samples 3 species, what is the probability that exactly 1 is migratory?

Discover the Hidden Mathematics Behind Nature’s Choice: A Probability Puzzle in Pond Ecology

Outside a quiet neighborhood pond, a scientist gently nets fish—curious about how species mix. Her question isn’t whispered in hushed tones, but carefully examined: Given a pond with 10 fish species, 4 migratory and 6 resident, if she samples 3 species at random, what’s the chance exactly one is migratory?

This is more than a classroom example—it’s a lens into how simple math reveals real-world ecological patterns. As public interest in environmental science and biodiversity grows, questions like this spark natural curiosity about how species inhabit shared spaces. With digital users increasingly drawn to intelligent, digestible facts about nature’s workings, this question sits at the intersection of science, probability, and everyday learning.

Understanding the Context

Why This Question is Resonating Online

Across the U.S., environmental literacy is rising—people explore how ecosystems function, driven by climate awareness, outdoor hobbies, and digital discovery. This pond sampling question reflects a growing trend: curiosity about how species coexist, migrate, and interact in balanced habitats. The mathematical framing makes complex ecological dynamics accessible, aligning with searchers’ intent for clear, credible explanations. With mobile-first consumption habits, concise yet thorough content performs best—prioritizing scannable structure and straightforward logic. This question captures that flow naturally, inviting readers to engage deeply without clickbait pressure.

Question: An ichthyologist studies fish in a pond with 10 species, 4 of which are migratory. If she randomly samples 3 species, what is the probability that exactly 1 is migratory?

Key Insights

How the Probability Works: A Clear Explanation

To find the likelihood that exactly 1 out of 3 randomly sampled fish species is migratory, we use combinatorics—breaking down how groups form.

There are 4 migratory species and 6 resident species. We want exactly one migrant and two residents.

Ways to choose 1 migratory from 4: ⁴C₁ = 4
Ways to choose 2 residents from 6: ⁶C₂ = 15
Total favorable outcomes: 4 × 15 = 60

Total ways to choose any 3 species from 10: ¹⁰C₃ = 120

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Final Thoughts

Probability = Favorable / Total = 60 / 120 = 0.5

So, the probability is 50%—a balanced outcome grounded in real-world ecology. This clear breakdown helps users grasp both the math and the science behind the scenario.

Common Questions Users Seek to Understand

Q: Since migration is rare (40%), why is there a 50% chance of finding exactly one migratory fish in a 3-species sample?
Probability isn’t skewed by rarity alone. Even sparse species appear in random samples; balance arises from multiple combinations, not single outcomes.

Q: Does this reflect real pond ecosystems?
Yes—this model mirrors how sampling captures population dynamics. However, real ponds include more variables like season, habitat, and human impact, which influence actual