5Question: An electrical engineer is designing a power grid with 5 substations. If 3 substations are chosen at random to install smart meters, what is the probability that a specific substation, say Substation A, is included?

Mon, 04 May 2026 02:16:53 +0000

**Why Smart Grid Upgrades Are Shaping Energy Infrastructure in America**
As the U.S. modernizes its aging power systems, engineers face complex challenges in optimizing reliability and efficiency. With growing demand for smart technology and renewable integration, one common question arises: what’s the chance a specific critical substation ends up among those equipped with next-generation meters? This isn’t just a math problem—it reflects the real-world decisions behind smarter, more responsive grids. With connectivity and data driving grid innovation, understanding the odds behind infrastructure planning helps stakeholders make informed choices. **The Probability Most People Overlook**
The question—“If 3 out of 5 substations are selected at random to install smart meters, what is the chance Substation A is included?”—invites curiosity about probability and resource allocation in public systems. Many focus on the numbers alone, but the real value lies in how this framework lays the groundwork for scalable, data-driven upgrades. Does Substation A stand a better or worse chance than others? The math reveals fairness in selection, even before technology activates the meters. **How the Math Behind the Probability Works**
To calculate the chance Substation A is included, consider how random selection functions. Choosing 3 substations from 5 is identical to choosing any one substation with equal likelihood. Since no substation has a built-in advantage, each holds a 3/5—60%—chance of being selected. This intuitive result reflects how probability balances fairness and predictability, essential in planning infrastructure where reliability matters. **Common Questions About Grid Selection and Fairness**
Many wonder: Why manual selection? Could randomness lead to uneven coverage? The truth is, modern utilities use rigorous criteria beyond chance—factors like load demand, aging equipment, and integration needs shape rollouts. Random selection is just one phase in a broader strategy, designed to ensure equitable, sustainable upgrades across diverse communities.