Urn A contains exactly 50 red balls and 50 black balls.This is one instantiation of the Ellsberg paradox. A moment’s thought should show that your probability on drawing red should be 50% (1:1 odds) in both cases. But we see that there is an intuitive tendency to prefer the wager in which the “dynamics” of the problem are known (Ticket A).
Urn B contains 100 red or black balls, but you don’t know the relative quantities. It might be 50-50, 0 red and 100 black, 100 red and 0 black, or anything in between.
You are offered two tickets. Ticket A pays $100 if a red is drawn from Urn A. Ticket B pays $100 if a red is drawn from Urn B. Which would you be willing to pay the most for?
- You would feel stupid if you chose Ticket B (the unknown urn) and it turned out that there were only black balls in Urn B. You have a strong preference not to feel stupid, so you’re willing to pay more for Urn A, which is guaranteed to be a “fair” urn. 
- You have been conditioned to think of a probability as a property of a situation, rather than a property of an epistemic state. (This is encouraged by our conventions of language, as in “the probability of rain tomorrow is 20%,” which uses the definite article “the” and thus implies a single uniquely correct value of probability, independent of what anybody knows about it. I prefer to phrase these things as “I give odds of 4:1 against rain tomorrow.”) For this reason, you feel that you do not know the probabilities for Urn B, and so you do not wish to bet on it.
- You are wary of being tricked by whoever is holding the draw into betting on a lame horse. An urn with unknown quantities of red and black seems like a potential trick.
If I am right, then in my opinion only one of these objections is defensible (number 3). But they do seem to me to do a half-decent job of explaining away this intuition.
“I don’t know. How long is a piece of string?”
“What about Laplace’s rule of succession? (s+1)/(n+2). Defining success as toothpaste and non-success as non-toothpaste, we get (2+1)/(3+2)=3/5 probability of toothpaste.”
“Yeah, I’m not sure that that is even applic - SQUIRREL!”
“Pay attention! How much would you be willing to pay for a ticket that paid out $10 if toothpaste was drawn?”
“I dunno, maybe I’d give $2.”
“Okay, so that implies your odds are 4:1 against toothpaste.”
“I think that reflects the triumph of curiosity over thrift, more than it does any real probability judgment. I would not pay $200 for a $1000 ticket. Or maybe I would.”
“Look, just answer this: how likely is toothpaste? You can see that 2 out of 3 things pulled out of the bag have been toothpaste. That is evidence that toothpaste is common in the bag.”
“If you say so. Do we even know that this is a random draw? Maybe the guy draws whatever he wants to, and that depends on how I bet. Why is he even performing this draw? He’s probably trying to trick me.”
“Trick you into betting for toothpaste, or against toothpaste? By the way, what’s wrong with the Laplace’s rule approach, again?”
“I don’t know. Please go boil your head.”