A renewable energy consultant is assessing a wind farm with three turbines, each capable of producing energy in increments of 1, 2, or 3 units per hour. What is the probability that exactly two of the turbines produce 2 units of energy in a given hour?

Sun, 03 May 2026 18:17:19 +0000

**Why Wind Farms Are Rethinking Energy Output Uncertainty**
In an era where reliable clean energy planning is critical, wind farm operators face a complex puzzle: predicting how turbines will perform under variable conditions. Each turbine generates energy in discrete increments—1, 2, or 3 units per hour—responding dynamically to wind patterns. For consultants assessing farm output, modeling these probabilities becomes essential for accurate forecasting and grid integration. Understanding how individual turbine outputs combine helps anticipate performance dips or surges, shaping investment decisions and operational strategies across the U.S. renewable sector. **How a Wind Farm Consultant Models Turbine Output Probabilities**
When analyzing three turbines, each operating in discrete energy brackets, predicting outcomes involves assessing independent performance patterns. Each turbine has three equally likely outputs: 1, 2, or 3 units. Calculating the likelihood of exactly two turbines producing 2 units requires examining all favorable combinations, using combinations and probability theory. This breakdown supports more resilient planning in volatile energy markets, helping stakeholders minimize risk and optimize output forecasting. To determine the probability that exactly two turbines produce 2 units of energy in an hour, each turbine independently has:
- A 1/3 chance to output 2 units
- A 2/3 chance to output 1 or 3 units Starting with three turbines, exactly two producing 2 units means one produces either 1 or 3. The number of ways to choose which two turbines produce 2 units is C(3,2) = 3.
For each favorable case, the probability is (1/3) × (1/3) × (2/3) = 2/27.
Total probability = 3 × (2/27) = 6/27 = 2/9.