A marine biologist is studying the population of a specific fish species in a coral reef. The reef contains 7 clownfish and 9 angelfish. If four fish are randomly selected for tagging, what is the probability that exactly

Thu, 30 Apr 2026 15:21:13 +0000

**Why Reef Populations Matter—And the Science Behind Fish Tagging**
More than just a pretty scene beneath the waves, the study of fish populations in coral reefs reveals vital clues about ecosystem health, biodiversity, and environmental change. As climate shifts and ocean pressures rise, understanding species distribution becomes crucial. One everyday example: how a marine biologist tracks fish such as clownfish and angelfish in a reef ecosystem. With 7 clownfish and 9 angelfish present, examining real-world tagging scenarios offers insight into probability and conservation planning—igniting curiosity in casual learners and environment-conscious readers across the US. Given that reefs face growing threats, data-driven studies help guide sustainable management. Tagging fish allows scientists to monitor biodiversity, migration, and population stability—tools that empower policymakers and communities. The chance of selecting specific fish combinations during sampling isn’t random; it follows mathematical principles that reveal patterns behind ecological sampling. **Understanding the Problem: A Statistical Glimpse into Reef Management**
The marine biologist’s scenario centers on selecting four fish from a reef containing exactly 16 total fish—7 clownfish and 9 angelfish. The key question is: what is the probability that exactly two clownfish and two angelfish are tagged? This practical example reflects real-world sampling methods used to estimate species abundance and manage coral reef health. By calculating this probability, researchers identify sampling fairness and refine conservation strategies. It also illustrates the role of chance in ecological studies and the precision required to protect fragile marine communities. Mathematically, this probability follows hypergeometric distribution since sampling occurs without replacement from a finite group. The reef’s mix of 7 clownfish and 9 angelfish sets a defined population. Drawing 4 fish at random, the task is finding the exact likelihood of capturing a specific split—this forms the basis for broader marine research and conservation planning.