Question: A GIS analyst is labeling 10 urban zones with binary codes of length 4 (each digit 0 or 1). What is the probability that exactly three of the zones receive a code with exactly two 1s?

Wed, 06 May 2026 07:02:43 +0000

**Understanding Urban Code Assignments: Probability in GIS Labeling Systems** Curious about how modern cities organize data amid rapid urban growth? A growing interest in efficient urban labeling systems has spotlighted a practical probability problem: How likely is it that exactly three out of ten designated urban zones receive a specific 4-digit binary code containing exactly two 1s? This question blends foundational data science with real-world GIS applications — essential for analysts mapping city infrastructure, planning services, or optimizing spatial datasets. While it may seem technical, mastering this probability reveals key patterns in binary encoding systems increasingly used in urban tech and smart city development. ### Why GIS Code Labeling with Binary Codes Matters Today In the age of geographic information systems (GIS), assigning consistent, unique codes to urban zones supports everything from emergency response routing to resource allocation and infrastructure planning. When cities label zones using 4-digit binary codes (each digit 0 or 1), each zone gains a unique identifier composed of only two active “1” markers — a compact yet informative system. Understanding the statistical behavior of these codes, such as how likely it is that three of ten zones end up with exactly two 1s, provides valuable insight into encoding efficiency and spatial data design. This knowledge helps planners minimize errors, avoid overlap, and optimize digital infrastructure crucial for smart urban growth.