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Probability is a difficult subject for me to grasp. I watch many religious vs atheist vs philosopher debates on YouTube where probability is often brought up, and because of my poor understanding I get confused.

It seems to me that probability is viewed differently in different situations. If I were to base a god claim on Bayesian statistics, an atheist would still not accept this because there is still a possibility it would be wrong. But in a different situation, say black jack, even with losing odds many people would still take this chance and play their hand against the house. ..Or if we use probability in a sport like basketball to guess how often a player will score a three pointer, we use it to somehow predict that they will probably do well again (and owners are willing to spend millions of dollars on the player).

I guess what I am looking for is how to fill this knowledge gap. if their are "Trial Cases" to better understand why people approach probability different in specific examples. What am i missing to better fill myself in on how to view probability better?

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I think you are confused because of usage of these term in English language. Rather than the mathematical standpoint.

To make this clear I am going to define each term (using Google dictionary).

  1. Probability : It is a mathematical term which is used to define the extent to which an event is likely to occur.

  2. Possibility : Is an English term used to define that something is possible or can occur.

  3. Gambling : It is also an English term used to define to take risky action in the hope of a desired result.

Now to understand the difference b/w Probability and Possibility.

Probability is generally used when we are talking about statistics. When you watch a debate of doctors or engineers or scientist they are more likely to use the world probability because they are usually talking about quantifiable objects.

Possibility is similar to probability but in possibility you can't determine the quantitative value. If you see a religious debate they are more likely to use word possibility or possible because they can't say for sure how much chance is there whether a god exists or not.

For E.g: If you flip a fair coin

Probability : 50% chance you get heads, 50% chance you get tails

Possibility : You might get heads, you might get tails, it might fall in sewer before you can see it, it might land vertically because it was stuck on a crack on the ground, etc.

There are endless possibilities however probability is limited. Lets take another example to get to understand to concept better.

What is the probability of a batter getting home run?
In this case both possibility and probability is applicable, because if you extract the history of a player and analyze it then you will get a mathematical value of his chances to score a home run. However actually hitting the home run is not only dependent on the batter but the relative skills difference b/w the batter and the pitcher, the mental state of the batter, etc.

Therefore it is possible that batter might hit the home run maybe say 60% (Now, how can we calculate 60% when the home run is not dependent on the batter only, because the batter got experience : he is used to play under stress, he practice daily and that makes him a consistent player.) It is possible that Michael Jordan (basketball player) plays extremely bad one day, it is possible but since he is a good player with good skills his probability of success is higher, the consistency of a player shifts the possibility to probability and that's why people spend millions on such players.

Lets take one more example, why does Dettol claims it kills 99.99% germs but not 100%, because even though the product is extremely good there is still a possibility that it might not kill germs, hence to save itself from lawsuits, companies claims to kill 99.99% or 97% etc.

The term possible and probable are use interchangeably because they are synonyms on some cases (depends on the context).

Talking about gambling:

Now lets say, that batter analyze the situation, he knows his team needs 2 points to win the game, 2 of the bases are covered. If he hits the ball far enough the 2 points can be gathered safely but the fielders are positioned far away in the field to stop this from happening, if he hits the ball close the guy on 2nd base won't be able to make the complete run. The batter is already on 2 strikes and knows that the pitcher is better than him. Now he might gamble to take a hard swing and try for a home run or loose the game.

The gamble here signifies that even when his probability of getting a home run is low he is willing to take the chances to win the game.

I hope it helped you clear the difference b/w the terminology

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  • "There are endless possibilities however probability is limited." that really helped me understand it better, thank you – Noah Jan 6 at 17:59
  • I am glad I was able to help – White Mars Jan 6 at 21:12
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I'm going to use some extracts from an article by Matthew H. Haber to explain the difference between possibility and probability. These extracts set out (some of the) different kinds of possibility; and with regard to probability, give a rough first indication of the (or a) distinction between objective and subjective probability. Haber also takes account of gambling and knowledge. I've added further references. I never normally answer by quotation but Haber's article is clear, compact, and informative: I hope it helps. It won't if you reject the idea or relevance of laws.

Possibility

How should we understand what is meant by "possibility" ...? Talk about possibility is talk about what is and what is not ruled out. But not ruled out by what? By what we know - epistemic possibility; by the laws of physics - physical possibility; by the laws of biology - biological possibility; and by the laws of logic - logical possibility. Underlying the above dialogue seems to be a concern over metaphysical possibility. Metaphysical possibility is that which is not ruled out by necessity; something is metaphysically possible just in case it is not necessarily not possible (Kripke, 1980; Jubien, 1997) (Matthew H. Haber, 'On Probability and Systematics: Possibility, Probability, and Phylogenetic Inference', Systematic Biology, Vol. 54, No. 5 (Oct., 2005), pp. 831-841: 833.)

Probability

Similar to the distinction made above between metaphysical and scientific possibility, so too is there a distinction between objective (or metaphysical) and subjective (or epistemic) interpretations of probability. Objective interpretations of probability are those that take probability to be a thing of the world that exists independent of us. Subjective interpretations of probability, on the other hand, take probabilities to be reflections of degrees of belief about a proposition of some event or object of the world. So subjective probabilities, then, do not exist in the world independently of our beliefs. A brief example can help draw out the importance of making this distinction.

Suppose, for example, that I had a coin that was known to be biased, though the direction of that bias was unknown. Suppose, too, that I asked both an objective and a subjective probabilist what the probability was that the coin would land "heads" upon flipping. The objective probabilist might respond with something like "if by 'probability' you mean objective probability, then all I can say of the biased coin is that the probability of that coin landing heads is not 50%. The actual objective probability of the coin landing heads is something that we can discover upon experiment and observation; but, given that the coin is biased, we know the probability cannot be 50%." The subjective probabilist, on the other hand, might respond to the same question as follows, "if by 'probability' you mean subjective probability, I have no reason for believing that the coin is biased either towards heads or tails, so the only justified degree of belief is that it is equally likely to be biased in either direction, and, thus, I can contingently assign a 50% probability to the proposition that the coin will land heads. Upon experiment and observation, we will be justified in adjusting our degree of belief accordingly." So if one is not careful to be precise about what kind of interpretation of probability is being discussed, there is great danger of mischaracterizing assignments of probability and confusing the issues at hand. In the example just given, both parties were right to gently chastise my ambiguous phrasing of the question, as the divergent answers given turned on which classification of probability was being assumed. (Haber: 833-4.)

Bayesian probability, mentioned in your question, is a version of subjective probability.

Gambling and knowledge

Take, for example, the gambler's fallacy: Roberto Alomar is batting 0.300. He comes to bat three times in a game and fails to get a hit. ... Our objective probabilist ... asserts that, because he is batting 0.300, he still has only a 30% chance of getting a hit, but this ... fails to take into account the full scope of knowledge. In the first place, because Alomar failed to get a hit in his last three times at bat, he is actually batting 0.297; the probabilities have changed, because they are historically contingent phenomena. More to the point, Alomar either will or he will not get a hit and there is no probability that can be assigned to that one event: betting on one event alone is foolish. (Siddall, M. E., and A. G. Kluge. 1997. 'Probabilism and phylogenetic inference', Cladistics 13: 332.)

References

Haber, M.H. 'On Probability and Systematics: Possibility, Probability, and Phylogenetic Inference', Systematic Biology, Vol. 54, No. 5 (Oct., 2005), pp. 831-841.

Jubien, M. 1997. Contemporary metaphysics: An Introduction. Blackwell Publishers, Malden, Mass.

Kripke, S. A. 1980. Naming and necessity. Harvard University Press, Cambridge, Mass.

Siddall, M. E., and A. G. Kluge. 1997. 'Probabilism and phylogenetic inference', Cladistics 13: 313-336.

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First and foremost, probability is a tool that agents use to make effective decisions. A gambler may use probability to guide his actions in the casino. An investor may use probability to value stocks. A patient or doctor may use probability to decide on a course of treatment.

Probability is described mathematically using probability spaces and random variables. We may prove objective statements about this formal concept of probability, according to the axioms of a probability space. When we apply probability to real-world events, probability is a useful model of an agent's lack of knowledge about some proposition.

Probability is not the only such model. Dempster-Shafer theory is one alternative, proving that probability is not the only possible formal model of uncertainty. Many agents do not use any apparent formal model for their lack of knowledge; do ants use an explicit probability distribution when deciding where the food might be? Probably not. Instead they, and also humans most of the time, rely on heuristics.

Probability is relative to what an agent knows. If you are told a die was rolled, the probability it came up 5 is 1/6. If you are told additionally it did not come up 3, the probability it came up 5 becomes 1/5. For someone else, who was told the die did not come up 1 or 2, the probability that same die came up 5 is 1/4. Probabilities are thus not absolute or physical things. They always have to do with the mind of some agent.

There is some controversy about the above claim when it comes to quantum mechanics or statistical mechanics. Are probabilities in these fields objective, and independent of agent? Maybe so; but probabilities in these subjects can also be understood as relative to what an agent knows. There may, however, be inherent physical limits on how much any agent can know about a subatomic particle or a box of gas molecules.

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My account will be not from the p.o.v. of mathematics, so it definitely will seem not "mainstream" answer.

Probability pertains to a fact. A fact is an event belonging to the past. When I realize or perceive an event as a fact (I would prefer to say, as facticity), I see it as if in the past mode and already accomplished, - even if it has not yet occured actually and is only prospected to occur in future or in abstraction. For, the future (just mentioned) of a fact is the future "in the past". That timeline can be prospected, which would be simply a reversed retrospection. Both the starting point and the outcome are considered perfected, "done". We cannot expect of a thing in that time-gauge. So what is the probability then? It is a device to disbelieve partly in the fact as "done". Probability 1 is actually the 0 magnitude protest against the fact, and the prob. 0.4 is the 0.6 units protest against it. The probability gauge is hypocritical because even under prob. 0 we still respect the fact as the fact in toto: our "protest" against facticity is a trick to better meet it and serve it. When we are presented with an acute fact, our immediate and momentary reaction is the feeling of disbelief, that is, the probability recoils towards 0, in order to swing then to 1 for us to be witness that we are impressed with (honour) the occurence. A scientist, when he "hopes" a probability of some unwanted event be near zero, "deep inside" is determined to greet the event in full, - because probability concept "assumes" the event already happened. This how knowledge - which is all about facts - works.

Possibility pertains to me. Possibility of a thing is my possibility of the thing (clouds outside the window are my possibility to get wet if come out or to get dull if don't). Having a possibility, I am engaged with (not "know" them) the object and with the whole world we both are in. Possibility directs to real (expectful) future, very different from the quasi future-in-past described above. Possibility is what makes me exist, which is the alias of saying that I'm temporal, not factual. Unlike probability, possibility is sooner quantum 50/50 ever, rather than continuous. And when it grows or reduces, that is because alternative possibilities hide or show, so we are speaking of saliences here, not of magnitudes. The 50/50 metaphor doesn't mean a "halfway" (as would be with probability); on the contrary, I'm 100% betrothed with it (the expected or apprehended state of the world-me-thing) and simultaneously 100% disconnected from it, - this is what usual calculus cannot valuate because a specific possibility is a condensation of nothingness: it is the agenda by the mode of promise-delay. It is important to remark, that possibility is about necessity (sounds paradoxical); possible thing is "needed" but delayed, and so it "sure" will come true if not impeded. It is pending in isolation without straps. Which is the opposite to a probability - this being absolutely unnecessary, as any facticity is. What is, is a surplus, and might become needed only through a possibility of something what isn't.

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