Considerations for choosing the correct hypothesis

This is too general a question. You're basically asking to study probability and hypothesis testing on one foot. If the machine drew one red ball out of a million black ones in a single attempt, I'd bet it wasn't "fair." Like a die that would land on a 5 a hundred times in a row. One-legged hypothesis testing: The criterion is probabilistic. You calculate probabilities for your two hypotheses, and choose the more probable one. Of course, you need to define the possible hypotheses before the discussion begins (and this is usually not done using probabilistic tools but rather based on knowledge of the circumstances and common sense).