If a shirt to wear is chosen at random, it means that every shirt had an equal probability of being chosen.
Not all the shirts may be in the set. You might think "I'm not going to wear a red shirt today" then pick a random one from what remains. The shirt is still chosen at random.
I think you and I have a different concepts of what random means. If you agreed with the prior sentences as per my last post, I will elaborate.
If a shirt to wear is chosen at random, it means that every shirt had an equal probability of being chosen. If I chose a shirt to wear for some unspecified reason, some unknown or unclear reason or it struck my fancy at the moment, it does not mean that it was chosen at random.I am including the second sentence in that section, even though I note that you are stopping at the first sentence. But I trust that you read the next sentence.
All shirts ARE in the universe of shirts that a person has to wear. Just as in the case of "all numbers between 1 and 100". If I remove one shirt or one number, it is an awkward technicality at best but boils down to rephrasing....ALL shirts except for this red one or all numbers between 1 and 100 except for 64.
In the example case, you now say that, after eliminating a red shirt from possible choices, "The shirt is still chosen at random." when you have presented absolutely no evidence at all that it was chosen at random. Why was it a random choice? What does a random choice mean in your example? it seems like the shirt was chosen and you are deciding it is a random choice because you are saying it is a random choice. It is as though randomness has no meaning at all, only outcome and any outcome is considered to be random. That's ok with me if you believe that, but I don't (and yes I am elaborating and interpreting to some extent but it is to make a point).
I very much disagree and stay with what I said and ask that you read it carefully.
If a shirt to wear is chosen at random, it means that every shirt had an equal probability of being chosen.
This remains coherent and accurate as per following from the first sentence. Because that is, in fact, a [generally accepted] representation of what random means.
Looking forward (not that you are saying it explicitly), it is not a meaningful argument against that sentence to say something like the probability distribution conforms to the list of probabilities associated with each of the possibilities of shirts to wear, so, even if you want to impose, after the fact, that what I am saying is wrong because you decide that there are different probabilities associated with each shirt because it is contrived to the point of being tortured.
We know that different outcomes can have different probabilities but the examples I used are clearly not talking about those distributions and you can tell by what I chose - I didn't say the green shirt has this probability and the white one this probability - they all have the same probability - how could anyone miss that?
Had I said there are 62 red shirts and 128 blue shirts and 4 green shirts and you picked 4 green shirts in 4 choices (without replacement) I could argue that it is not a random choice based on an unlikely outcome and the common theme that each shirt has the same probability of being chosen - but in fact, it could be a random choice no matter how extreme the outcome. That is not the point here.
You know what it means to pick a shirt at random and to pick a shirt for some other reason and SAY something like I chose this shirt at random - that is my point....look at the following sentence...
If I chose a shirt to wear for some unspecified reason, some unknown or unclear reason or it struck my fancy at the moment, it does not mean that it was chosen at random....and it most definitely does not mean it was chosen at random because I am stating outright that there was a reason, specified or not, and most definitely that is NOT evidence of a random choice.
Edit: to add two examples: 1) I stand in front of my closet and look at all my shirts and think about the colors and matching with my pants and comfort and and trying to get laid and looking cool or looking for something that goes with a cowboy hat or for some reason choose a shirt. and 2) I stand blindfolded in front of the, arm outstretched and waving back and forth over the totality of my shirts until somebody somewhere (who isn't watching any of this) yells "stop". Then I pick the shirt closest to my outstretched hand.
If used 1 and went to work and said "I chose this shirt at random". I would peeve myself off because I would be misusing the word and disrespecting the process which I hold dear to me.
If I used 2 and went to work and said "I chose this shirt at random". I would not peeve myself off because it was at least approaching a random process.
Note that my peeve is not based on randomness vs. causation, it is simply the MISUSE of the word which underscores the common misunderstanding and under-appreciation of the meaning of the word,
in my view.
So, no, it does not look like we agree.