What is a mathematical or logical name for the process of proving a statement by exhausting the domain?

I am trying to understand logic and I came across a set of actions that I describe below that I can't get my head around.

```Suppose you have a bag of multiple colored balls.

Situation 1.
Argument: There are no red balls in the bag.
Action: Pick up balls at random until you find a red one.

Situation 2.
Action: Pickup a random ball from the bag.
Argument: All the balls in the bag are of same color as the ball you picked up.
```

I have some questions.

1. What is the correct conclusion in each situation?
2. Are these situation logic related?
3. Can one be converted to another?
4. Which is correct and which is flawed?
5. What are the names for the logic contained in these situations?
• What logic? I can't get my head around it either. What are the premise? What is the conclusion? Feb 14 '12 at 14:59
• I don't really understand how this question is posed, least of all the "situations". Could you elaborate on these? (Normally, arguments consist of premises and conclusions) Feb 14 '12 at 16:01
• Is there any chance I might be able to persuade you to clarify the headline here a bit? (They should ideally encapsulate or at least reflect some of the specific content of the question) Feb 14 '12 at 16:25
• @seamus , stoucfury I am sorry. I know there has to be a conclusion but I don't know what followed them and didn't want to post nonsense. May be I'll add it as another question.
– Dirt
Feb 14 '12 at 20:16
• @Joseph whether this is flawed was the main question and others were for better understanding, so I posted it that way. I didn't know how to frame a question that reflected what it described.
– Dirt
Feb 14 '12 at 20:20