Question: A science administrator reviews 10 research proposals, 3 in AI and 7 in biotechnology. If 3 proposals are selected at random, what is the probability that at least 2 are AI-focused?

Sat, 02 May 2026 22:10:41 +0000

### The Evolving Landscape of Research Funding and Strategic Decision-Making
In an era defined by rapid technological advancement and heightened focus on innovation, decisions about research funding are shaping the future of industries across the United States. For science administrators, selecting high-impact projects involves balancing emerging fields with proven disciplines, guiding investment toward breakthroughs that drive progress. With AI accelerating digital transformation and biotechnology transforming healthcare, understanding how funding choices are evaluated is more relevant than ever. This dynamic environment increases interest in core statistical reasoning—especially when assessing probabilities tied to strategic proposals. One such calculation reveals insights about risk, diversity, and impact: when reviewing a pool of 10 proposals—3 in AI and 7 in biotechnology—what remains probable about selecting at least two AI-focused studies? #### Why This Question Reflects Broader Trends
The convergence of AI and biotechnology represents a frontier where interdisciplinary innovation fuels growth. AI serves as a powerful accelerator in biological research, from drug discovery to personalized medicine, making its role increasingly central. Yet biotechnology remains foundational, with applications in disease treatment, sustainable agriculture, and advanced materials. Within U.S. research funding contexts, understanding the likelihood of selecting a subset of AI proposals informs strategic allocation and risk assessment. As organizations strive to balance short-term impact with long-term potential, evaluating such probabilities supports data-driven decisions that align with scientific priorities and economic realities. #### How the Probability Calculation Works
The query centers on a combinatorics model: selecting 3 proposals at random from a total of 10, 3 of which are AI-driven and 7 are biotechnology-focused. The goal is to determine the probability that at least 2 of the 3 chosen proposals are in AI. This involves assessing two key scenarios: exactly 2 AI proposals and exactly 3 AI proposals, then combining their probabilities. The STATistical foundation ensures accuracy while keeping complexity accessible—ideal for curiosity-driven mobile users seeking clarity. By translating abstract math into tangible insights about decision frameworks, this approach supports informed engagement without overwhelming readers. #### Deep Dive: What the Numbers Reveal About Risk and Selection