When Is Probability Absolutely Certain?

In a post from last year titled Judgments Of Probability [1], I explained how probability judgments about things like whether or not it is about to rain or whether or not a person who jumps will fall back to the ground are purely subjective and speculative, rooted in past experiences which the future does not have to imitate by necessity.  A great number of probability judgments fall into this category.  When people say that a thing will "probably happen," they almost always mean that it only seems to them as if that thing will happen because of some experience or set of experiences they have had.  There is no way to calculate the actual probability of whether or not gravity will hold in the future or if dark clouds mean it is about to rain.

But there are some conditions where someone can have absolute certainty about the probability of a certain outcome--but this occurs only in very select scenarios, most of which are utterly unlike scenarios such as predicting the weather, estimating if scientific laws will hold in the future, and so on.  Let's do some thought experiments to demonstrate this.

You hold a shuffled deck of 52 cards, all of them facing away from you, and only two of the cards are jokers.  What is the probability that you will get a joker by lifting up the top card?  If these conditions are met, then the probability is exactly 2/52, or 1/26.  This is infallibly certain.  Another thought experiment involves a group of 20 people over the age of 18.  If five of them are 80 years old, then the probability of someone who is 80 years old being chosen at random from the group is 5/20, or 1/4.

If a quarter has two sides (heads and tails) and it must
land on one side if thrown, then there is an exactly 50%
chance that it will land on either heads or tails.

Now, yes, I realize that it is impossible for me to prove that an actual deck of 52 cards doesn't change while I'm not perceiving it, and therefore this absolute certainty about probability is attainable in thought experiments only, not interactions with the external world.  I realize that I can never actually prove the exact age of another person, nor can that person prove his or her age to me.  But the concepts of what I have described are still true by necessity--in some situations (even just situations in thought experiments), the exact probability of a certain outcome can be proven in full.

Notice that the thought experiments I used as examples are completely different than quite a few of the situations where people claim that something is probable or improbable.  There is no way that I can prove it is objectively probable, for instance, that a girl is romantically interested in me, only that it is objectively true that it seems to me like she is.  See the difference?  Estimations of romantic attraction can be made despite a plethora of unknown variables, whereas the strictly logical/mathematical calculations in the thought experiments I provided can be proven abstractly, without me even being in the situations themselves.

Probability is still often a thing perceived on the basis of subjective experiences, but in some cases it is absolutely knowable.  It just depends on the conditions of the situation--and often conditions and variables are not fully known.


[1].  https://thechristianrationalist.blogspot.com/2017/04/judgments-of-probability.html