Question: A science policy analyst must evaluate 9 proposed initiatives, 3 of which focus on renewable energy. If they randomly select 4 initiatives for further review, what is the probability that at least 2 of them focus on renewable energy?

Sun, 03 May 2026 01:26:23 +0000

**Why Policymakers’ Renewable Energy Choices Matter—A Deep Dive** As debates over climate resilience and clean energy accelerate across the U.S., the role of science policy analysts has become increasingly vital. With major federal initiatives unfolding, understanding how proposed projects are distributed—and identifying opportunities where renewable energy receives strategic focus—demands data-driven clarity. A straightforward yet revealing question returns repeatedly: if a science policy analyst randomly selects four initiatives from a slate of nine, and three are renewable energy-focused, what is the likelihood that at least two of the selected initiatives are renewable? This probabilistic lens uncovers not just numbers, but insights about priority-setting in a pivotal moment for energy policy. **Understanding the Numbers Behind Renewable Prioritization** The scenario involves a total of 9 initiatives: 3 dedicated to renewable energy and 6 belonging to other sectors. The analyst’s task is to pick 4 at random. To calculate the probability that at least 2 of these selections focus on renewables, a combinatorial approach reveals key patterns in risk and representation.