[TomCowley]

Saying that the situation is "only theoretical" is your standard nihilist irrelevant nonsense. "An event will either happen or it won't. What is the probability that it will happen?" You can draw absolutely no bias from the description, any more than you could if you were told there were two outcomes, frumplesnort and dingleberry, described in a language incompehensible to you, and you were asked for a probability. ANSWER the question as it DOES exist, don't say it can't exist.

Monty Hall is a MISapplication of sklansky's principle. If you couldn't assumethat all 3 doors were equally likely to begin with (skalnsky's principle), then you couldn't solve the problem at all.

Two Envelopes is not a mathematically valid problem. When converted into a mathematically valid problem using limits, guess what the odds asymptotically approach? That's right, 50%.

The third and fourth cases are simple math ignorance about how to calculate conditional probability (if shown this problem from a frequency standpoint, even relative idiots can understand the process, although they'll be shaking their head at the answer). It has nothing to do with Sklansky's principle, and is certainly no sort of counterexample to it. If you list the FOUR indexed outcomes, boy-boy, boy-girl, girl-boy, girl-girl, even idiots should get this right.

Some people are godawful at math. DS has nothing to do with this. Please tell me where you teach, so if I ever have kids, I can make sure they don't end up in one of your classes. The last thing I'd want is somebody who can't analyze trivial situations and instead has to resort to "we just have to know something about the outcomes by what they are" gobbledooygook gibberish.