Question: An agri-tech company tests 4 soil sensors and 2 weather stations for a sustainability project. If they activate 3 devices randomly, what is the probability that exactly 2 are soil sensors and 1 is a weather station? - Decision Point
An agri-tech company tests 4 soil sensors and 2 weather stations for a sustainability project. If they activate 3 devices randomly, what is the probability that exactly 2 are soil sensors and 1 is a weather station?
An agri-tech company tests 4 soil sensors and 2 weather stations for a sustainability project. If they activate 3 devices randomly, what is the probability that exactly 2 are soil sensors and 1 is a weather station?
In the evolving landscape of precision agriculture, small-scale tech trials play a key role in shaping sustainable farming. One such real-world scenario involves an agri-tech company deploying a mix of four soil sensors and two weather stations to monitor environmental conditions. When three devices are randomly activated, understanding the likelihood of specific combinations offers insight into how data is collected and prioritized in real farming operations. This probabilistic scenario, while technical, reflects broader trends in tech-driven resource management across the U.S. farm sector.
Why Does This Question Matter Now?
Sustainability is no longer a niche concern—it’s central to agricultural innovation. With growing pressure to reduce environmental impact and improve resource efficiency, monitoring soil health and weather patterns has never been more critical. Trials testing multiple sensor types help optimize water use, fertilizer application, and carbon management. Activating devices randomly simulates low-resource testing environments, mirroring how startups and researchers validate new tools on limited datasets. As farmers and agribusinesses adopt smarter systems, knowing how probable specific device mixes are offers a practical lens into tech reliability and performance.
Understanding the Context
How Does the Probability Work?
To calculate the chance of selecting exactly 2 soil sensors and 1 weather station from 4 soil sensors and 2 weather stations activated from among 6 total devices, we use combinatorics. The total ways to choose 3 devices from 6 is 6 choose 3, which equals 20. The favorable outcomes require choosing 2 soil sensors from 4 and 1 weather station from 2—calculated as (4 choose 2) × (2 choose 1
