Question: An ichthyologist studies 12 Arctic fish species, 4 of which are vulnerable to warming waters. If 5 species are randomly selected, what is the probability that exactly 2 are vulnerable?

Sun, 03 May 2026 03:02:11 +0000

**An ichthyologist studies 12 Arctic fish species, 4 of which are vulnerable to warming waters. If 5 species are randomly selected, what is the probability that exactly 2 are vulnerable?** Recent climate shifts are reshaping Arctic ecosystems at an accelerating pace. As ocean temperatures rise, species stress grows—especially in fragile habitats where expert knowledge helps predict impact and guide conservation. Now, a probabilistic question emerges that combines biodiversity, statistics, and environmental change: What is the chance that exactly 2 out of 5 randomly chosen Arctic fish species are among the 4 vulnerable ones? This question sits at the intersection of real-world fish ecology, statistical modeling, and climate science—making it both timely and relevant for US audiences concerned with sustainability, marine health, and data-driven insights. Diving into the numbers, this scenario follows a classic hypergeometric distribution. There are 12 total Arctic fish species, 4 classified as vulnerable, and 8 others considered stable. When selecting 5 species at random, we want exactly 2 vulnerable and 3 stable. This specific combination invites deeper curiosity about chance, risk, and marine resilience. ### Why This Question Matters Now