How we determine facts.

[Heywood]

Actually, no. My dog makes conclusions from one or two incidents. She makes some odd conclusions, such as all men with beards are bad. So do some people, particularly children and the superstitious. Science, on the other hand, is based on not drawing unwarranted conclusions. Instead, you make a hypothesis based upon the data (which ought to be a better sample than three) and then proceed to test the hypothesis (by either designed tests or by looking for contrary evidence).

Actually yes,

Suppose a planet was observed orbiting Proxima Centauri.....let call this planet Pandora. Further suppose on that planet was observed a collections of complex and intelligent beings, bi-pedal and blue skinned. The conclusion would be that intelligent life pervades the universe. This would be the scientific consensus even though it is certainly possible that the only intelligent life in the universe is on Earth and Proxima Centauri.

---

In the case of three marbles in a bag, all you have to do is look at all the marbles. Guessing about one marble at a time would be silly. Sampling hundreds of bags might tell you something about the likelihood of marble in the bags in that area.

But let's make this a more likely scientific problem. You find a bag of three marbles in a 1000 year old tomb. Two of the marbles are black, one white. What do you conclude? They had marbles. Find more bags in more tombs and you might form a hypothesis about the marbles. If there are more white marbles than black by two to one, you might conclude that black is more costly and begin to look at the resources necessary to produce white as opposed to black. If it's always two white and one black in every bag, you might look for symbolic meaning or evidence it was part of a game. And so on. You might never figure it out. But you probably would at least falsify a few hypotheses.

If you always found three marbles two white and one black and found directions for playing a game of chance with the devil involving two white and one black marble, and a mural showing the devil playing the game in another tomb, you'd be well on your way to a theory about why there are always two white and one black marbles in each tomb.

---

I used three marbles because it made the math simple. I used drawing marbles out of bag one by one because I needed observations. The point is each observation that is consistent with a conclusion adds to the confidence that the conclusion is correct.