There is actually. Its called a T distribution table. If you ever have the pleasure (or agony) of taking a college statistics course, you will learn that there are "probabilities of probabilities happening within X number of attempts".

For example, we know that a coin can flip to heads or tails right? That's a 50% probability. But does that mean every other coin flip comes up on the other side? No. In fact, we can get heads multiple times in a row. T Distribution tables give you the probability of this happening. So for example, even though a coin flip is 50%, what is the probability that out of ten flips, all coins come up heads?

I hope this answers your point!

With thanks for your answer;
I mean that there are many cases in which, when we calculate and get a probability ratio number like that; P(A),but
in real for Pa(A) less than P(A),the absolute and certain answer is Pa(A) .

I mean that there are many cases in which, when we calculate and get a probability ratio number like that; P(A),but
in real for Pa(A) less than P(A),the absolute and certain answer is Pa(A) . — boby

Sorry, I'm lost. Its been years since I took a statistics class, and a google search did not easily reveal what P(A) and Pa(A) were.

So P is the probability of A (our thing happening). Does Pa stand for the Probability Actual of thing thing happening?

So if we say its a 50% chance that something happens over 10 flips, but the actual probably is 13%?

If this is the case, this is described by "Standard deviation", which is the understanding that our probability has a likelihood of varying a certain degree over X number of attempts.

Meaning that if I have a 50% chance of something occurring, and I flip the coin once, the pa(A) would be 100% heads with one iteration. The more iterations we do of the coin flip, the lower the standard deviation becomes with different calculations.

But at this point I'm not sure this is a philosophy question anymore, but a statistics question. Statistics has been utilized for centuries, I'm quite certain that what you are trying to ask a question about has an answer there.

Hello,

In probability math,because of math's nature that is merely quantitative and not
a qualitative, for any case,it give you just a number; so, I think for every cases, there should be a boundary probability number that is " meaningfulness " just for that specified case and out of that boundary is not meaningful and that is just a meaningless number. — boby

Being that peobability is defined as = (number of outcomes in the event space (E)/number of outcomes in the sample space (S)), it follows that the calculated probability is meaningless when S = 0 or S = infinity as division by these "numbers" are undefined.

Examples:

1. Intelligent Design: The probability that a physical constant has the value that it has = 1/infinity

2. Cards: The probability that a card is 3 given that it's a blue card = 0/0

With thanks for your answers;

I meant that ; sometimes we get a probability ratio of for example of : 1/ 5 ∧ 23 from a calculation

but,in fact,a number of; 1/ 5 ∧ 8 for that is perfectly the absolute answer.

With thanks for your answers;

I meant that ; sometimes we get a probability ratio of for example of : 1/ 5 ∧ 23 from a calculation

but,in fact,a number of; 1/ 5 ∧ 8 for that is perfectly the absolute answer. — boby

Are you talking about significant digits? So lets use the decimal system for a second.

We do a calculation that shows we need to make a board 1.0000000000001 meters long. But we just round it to 1.0. Is that what you mean by meaningfulness?

If so, we use significant digits depending on our need for accuracy. That depends both on how accurate you need the measure to be, and how accurate you can actually use. If I have a meter stick, nanometers are pointless to me, because I cannot measure in that. And if I really only need something to be within a few millimeters of a meter, nanometers are also pointless, so we don't use them.

Did that answer what you were looking for?

Did that answer what you were looking for? — Philosophim

No. He wants the probability to have limits of range that's meaningful. And I don't know how that happens.

Yes,you are right with the following extra explanation that ;
We faced to a few cases(events),in our real life daily,that their occurrences are inevitable
but their math probabilities are still get you numbers that show uncertains!!

We faced to a few cases(events),in our real life daily,that their occurrences are inevitable
but their math probabilities are still get you numbers that show uncertains!! — boby

If something is certain, then it is a 100% probability. Having a probability less than that means it is uncertain, and not inevitable. I am still uncertain of what it means by probability having a limit of range that is meaningful. Still, perhaps at this point you should go to a math forum. I think we're out of the bounds of philosophy at this point.

That doesn't follow. The exact value is either $\frac{1}{5}^{23}$ or $\frac{1}{5}^8$. It cannot be both numbers at the same time.

there should be a boundary probability number that is " meaningfulness " just for that specified case and out of that boundary is not meaningful — boby

I'm not sure what meaningful means in a probabilities context. I think of probabilities as arising from the analysis of purely hypothetical mathematical possibilities.

When I think of meaningfulness I look at the application of the numbers to experience in an ordinarily setting. Perhaps a personal or social phenomenon is looked at to see if numbers can be fitted to repeated occurrences or chain of events. Then meaningfulness can be thought of as a measurable degree of fitness of the two models, one for the world and one from math.

Probability arose from gambling which in many cases, it can provide an accurate and reliable model of the relative long-term frequency.

Also, the OP's question doesn't really have much to do with probability, as ratios are not necessarily probabilistic.

Probability arose from gambling — ReluctantMathematician

So probabilities would be meaningful as applied to gambling, for example, or are they meaningful just as numbers?

Probability is widely and commonly used in applied mathematics.