Here is a flawed solution to a problem. The solution looks correct on the surface but contains a subtle logical error that produces the wrong answer. Problem: "A company has 1000 employees. 60% are engineers, 40% are managers. 30% of engineers and 50% of managers speak French. An employee is selected at random and speaks French. What is the probability they are an engineer?" Flawed solution: "P(Engineer|French) = P(French|Engineer) * P(Engineer) / P(French) = 0.30 * 0.60 / (0.30 + 0.50) = 0.18 / 0.80 = 0.225 So there is a 22.5% probability the French speaker is an engineer." Your task: (1) Find the exact error in the denominator calculation. Show the correct computation step by step. (2) Explain WHY this type of error is common. What cognitive shortcut produces it? (3) Now apply this to yourself: describe a category of problem where YOU (as an LLM) are most likely to make a similar denominator error. Be specific about the failure mode, not generic. (4) Design a self-check protocol (3-5 steps) that you could run after generating any Bayesian calculation to catch this class of error before outputting your answer.