In your volume example, imperial units only divide cleanly for certain factors (e.g. 2 in your example), from certain starting points (e.g. two pints) and within certain ranges (keep dividing a cup by 2 and it stops dividing cleanly).
They have the 40 minutes rule for reasons of efficiency, the policy is clearly stated so I don't see why you were upset - you should arrive earlier. As for the fog, not much Ryanair can do about that I'm afraid.
"This usually leads me down a path of questions that result in me having to teach myself something to build something to solve a particular problem which fulfills a need." - but better make a quick post to hacker news first.
Which makes more sense: owning one quality $100 knife for 30+ years, or going through 10 $20 knives over the course of 30 years?
It depends. The $100 knife could become lost, stolen or damaged. Improved or cheaper knives, or even a new technology to replace the knife as we know it, could appear in the next 30 years. You could even keep two cheap knives so you have a spare whilst the other is in the dishwasher.
"Or another example that I think speaks more directly to your post: you see a woman with a T-shirt reading "Proud Mother of Two" next to a girl who is obviously her daughter. What is the probability of her other child being a boy? Again, since there are twice as many mixed families as pure girl families, the odds are 2/3."
The odds are 50%, do you seriously think different?
Your mistake is that in families 1-250 the girl next to the mother could be either daughter.
In families 1-750 there are 1000 daughters, the daughter standing next to the mother is equally likely to be any of those and half have brothers, half have sisters.
Think about it this way: I take two coins out of my pocket and hold them inside my hand so that neither of us has seen them. I show you the coin in my left hand and you see that it is tails, what are the odds of the coin in the other hand being heads? 50%. This is the chance of a head/tail combo in this case.
I now put the coins back into my pocket, shuffle them about, and again take them out inside my hands. This time I look inside both my hands, not letting you see, and tell you (truthfully) that at least one is tails. Given that information, you can deduce three mutually exclusive possibilities each of equal probability - both are tails, only the coin in my right hand is tails or only the coin in my left hand is tails. Hence we have the odds in this situation of 2/3 for a head/tail combo.
It is easy to see that the first situation is akin to knowing that a particular child is female, whilst the second is akin to knowing that at least one of the children is female. Also, in either case it does not matter if the coins are distinguishable - one could be a euro and the other a pound.
No, that is not it. With G'g and Gg' you are repeating the same permutation in your set above!
It makes no difference if they have distinguishing marks or not. It matters if you are told that a particular child is a girl (50%) or if you are only told that at least one child is a girl (66%).
The difference is that you have specified that the child picked up from the police station is a girl, thus only the sex of the other child is unknown. This other child is either a boy or a girl, presumably with a 50/50 chance either way, resulting in a 50% chance of one being a boy and one being a girl. Concretely, using a capital letter to denote the sex of the child picked up from the station, there are only two possible permutations Gg and Gb, each of equal probability, and 50% of those are girl and boy (Gb). On the other hand if we only know that at least one is a girl we have the permuations, gg, gb, bg - resulting in the 66% chance.
"Both of my kids are driving me crazy! Just yesterday I had to pick one of them up from the police station--I grounded her for a month!" - given just the information in your quote, the odds are 50% of a boy and a girl.
His point is that a person telling you they have one girl would be accepted as referring to a particular child. Thus, BG and GB merge and the odds are 50% of a boy and a girl.
"To the contrary, the warning labels backfired: they stimulated the nucleus accumbens, sometimes called the 'craving spot,' which lights up on f.M.R.I. whenever a person craves something" - maybe they were craving to be non-smokers.