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? - Sterling Industries
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?
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.
Understanding the Context
Why This Question Matters Now
Climate change exposure is no longer abstract—especially in the Arctic, warming waters threaten species differently. The US scientific community and environmental platforms highlight vulnerable fish not just as casualties, but as indicators of broader ecosystem shifts. With public interest in ocean health rising, inquiries like this reflect an intent to understand risk, adaptation, and biodiversity trends. This data-driven curiosity fuels science engagement without crossing into alarmism, aligning perfectly with Discover’s mission for informed, low-friction learning.
How the Probability Actually Works
Rather than random chance, this question reflects careful statistical modeling. The hypergeometric distribution calculates probabilities for drawing specific groups from finite populations—ideal for rare, fixed groups like 4 vulnerable species among 12.
Key Insights
To compute:
- Total ways to choose 5 species from 12: C(12,5)
- Ways to choose exactly 2 vulnerable from 4: C(4,2)
- Ways to choose 3 stable from 8: C(8,3)
The probability emerges as:
C(4,2) × C(8,3) ÷ C(12,5)
C(4,2) = 6, C(8,3) = 56, C(12,5) = 792
Probability = (6 × 56) ÷ 792 = 336 ÷ 792 ≈ 0.4242, or 42.4%
This precise probability
