There is more to it, even to seemingly out-of-place words like род (type, gender, kind). Many words in Russian are made from the same parts. Про + пуск also allows you to make a good guess what verbs пускать and пропускать may mean, maybe even выпускать and допускать. :)
Where I first worked in 1993, I would join the line in the lobby and push the button E74 when I reached that point (my пропуск would fall from its slot onto the conveyor belt below). When I had reached the window, the old woman would pick up the next пропуск, look at the photo on it, look at me, and say, "Доброе утро, Иван Иван'ич!" I would nod and answer, "Доброе!" as she handed the pass through the slot under the window and pushed the button to release the turnstile.
Interesting how отпуск ‘semester, vacation’ and пропуск have similar endings.
Also consider впуск, выпуск, допуск, запуск, напуск, опуск, перепуск, попуск, подпуск, предпуск, припуск, распуск, спуск, and упуск.
Some of which are not found in dictionaries and have zero hits in Russian National Corpus. What I mean, it is completely fine to not know half of these words.
Unfortunately, all will soon (in a few weeks) be found by a Google search (at least once). ;)
I actually searched all of them on Google, the only ones of those words that did not appear were упуск and распуск.
роспуск would be the word.
The only useful words of these are выпуск, допуск, запуск, спуск and роспуск. Some of the others exist as specialised vocabulary some native might now if they are familiar with the field (I didn't even know these words exist); a few apparently do not exist in any meaningful way. On the other hand, native speakers can occasionally coin a new word ("outmergement") provided others can guess the meaning in the context.
It is pretty logical given the base meaning of "пускать" and then the verbs отпускать and пропускать. Letting someone go away ("letting out" "letting go") and letting someone through do have something in common if you look at them from that perspective.
Does this only mean pass when that has essentially the same meaning as permit i.e. a permanent document giving one permission to do something? Or does it cover a one-time "pass", such as a "hall pass" (a permission slip allowing a pupil to be outside the classroom, because, for example, they need to visit the cloakroom - which applies only right now and not at any future point)?
Both. A permanent пропуск usually has your photo on it, may be laminated, or may be small booklet. A one-time pass (a "visitor" pass) is authorized by someone with appropriate authority and may require being accompanied by an escort.
In the first place where I worked in Moscow, my пропуск never left the premises. I surrendered it to get out of the building, and I punched the button labeled Е74 in a large rectangular array of buttons (which caused my пропуск to drop out of its slot onto a conveyor belt to be carried to the guard at the window) in order to receive my "pass" for entrance.
Both. A one-time pass is "однора́зовый" or "ра́зовый" пропуск, or more rarely "разрешение на проход"
Thank you both. I notice you are giving examples of passes/permits that give access to somewhere, such as a workplace. Is пропуск also used for a permit that gives you the right to use something - such as a 'resident's parking permit' (or the "residents' permits" that allow only people who live within certain areas of British capital cities to drive toll-free on certain roads at certain times)?
You see, пропуск is derived from the verb пропускать "to let through"...
That is why etymology is so useful... :) It limits it to physical, not metaphorical, access.
Is пропуск genitive or accusative here? Why isn't the declension for пропуск?
Here пропуск is nominative, and it is the subject of the Russian sentence. Literally, in Russian word order, the question is "By you is permit/pass?"
Possession is commonly expressed in Russian with the possessed object in the nominative case and the possessor in the genitive case governed by the preposition "у" (by, next to): У меня книга. У меня пропуск. У меня кот. There is also a verb иметь meaning to have or possess, and it takes the accusative case: Я имею книгу. Я имею пропуск. Я имею кота.
Notice that the accusative form of inanimate masculine nouns is the same as the nominative form, and the accusative form of animate masculine nouns is the same as the genitive form. By the way, "я имею кота" strikes me as really strange, and I would always say "у меня кот".