Question: A climate scientist analyzes 10 years of ocean temperature data from the Great Barrier Reef and selects 4 years at random to study extreme heat events. If 3 of the 10 years show record-breaking temperatures, what is the probability that at least 2 of the selected years are record-breaking? - Treasure Valley Movers

Why Record-Breaking Ocean Temperatures Matter for the Great Barrier Reef

Climate scientists track ocean temperatures across decades to uncover patterns in extreme heat events—especially as rising ocean temperatures threaten vulnerable ecosystems like the Great Barrier Reef. With rising global temperatures, marine heatwaves have become increasingly common, placing coral communities under growing stress. Understanding which years stand out—particularly when extreme warmth recurs—helps researchers identify high-risk periods and refine long-term conservation strategies. This data-driven approach reveals critical insights about the reef’s resilience and vulnerability in a warming world.

How Does This Probability Question Reflect Real-World Risks?

The scenario presents a practical risk assessment: a climate scientist randomly selects 4 years from a decade in which 3 years had record-breaking ocean temperatures. The core question explores the likelihood that at least 2 of those 4 sampled years were among the extreme three. This type of analysis matters because it quantifies uncertainty in climate data—helping scientists and policymakers prepare for future shocks. When even a small subset of years experiences occasional extreme heat, climate models suggest increasing frequency; this form of statistical modeling supports early warning systems essential for reef protection.

Mathematical Insight: Calculating the Odds

To determine the probability that at least 2 of the 4 randomly selected years are among the 3 record-breaking years out of 10, we apply standard probability theory using combinations.

We assume simple random selection without replacement. The total ways to choose 4 years from 10 is C(10,4) = 210.

To have at least 2 record-breaking years, two cases apply:

• Exactly 2 record-breaking + 2 normal years: C(3,2)*C(7,2) = 3 * 21 = 63
• Exactly 3 record-breaking + 1 normal year: C(3,3)*C(7,1) = 1 * 7 = 7

Total favorable outcomes = 63 + 7 = 70
Probability = 70 / 210 = 1/3 ≈ 33%

This result reflects the moderate risk—less than half—of encountering multiple extreme heat years in a routine sampling. It supports real-world decision-making by grounding uncertainty in data rather than speculation.

Understanding Scientific Sampling and Risk

Random sampling from a known dataset offers a fair snapshot of broader trends. For scientists analyzing decades of reef data, such methods validate observed patterns and ensure statistical credibility