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Probabilty vs. Possibility

eijah

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A probability can be from 0 to 1, but what about a possibility?

That is, is a possibility either 0 or 1? Or can a possibility also be from 0 to 1? Note: I am not talking about conditional probabilities, or am I?
 
Just joking.

Assuming this is a serious question, then, I'm not aware of a mathematical "possibility theory". The way I tend to hear it used in everyday speech, "X is possible" is basically synonymous with "the probability of X is not zero", and "X is impossible" is synonymous with "the probability of X is zero".
 
eijah said:
can a possibility also be from 0 to 1?
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In some circumstances we can reasonably indicate possibility as a percentage between 0% and 100% -- but then you can decide to interpret any percentage less than 100% as zero.

For example, if you ask whether it is possible for a factory to produce 100,000 automobiles per year, the answer might be that it is 60% possible. It can produce 60,000 per year, so it can fulfill 60% of your requested objective, which is more than 0% of the objective, after all.
 
ctamblyn said:
Just joking.

Assuming this is a serious question, then, I'm not aware of a mathematical "possibility theory". The way I tend to hear it used in everyday speech, "X is possible" is basically synonymous with "the probability of X is not zero", and "X is impossible" is synonymous with "the probability of X is zero".
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This.

JJM 777 said:
For example, if you ask whether it is possible for a factory to produce 100,000 automobiles per year, the answer might be that it is 60% possible. It can produce 60,000 per year, so it can fulfill 60% of your requested objective, which is more than 0% of the objective, after all.
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No, I'd say then, it's not possible to produce the 100,000 cars.
 
Let's take a coin flip. Let's say we have a standard American quarter and a nice solid table on which to flip it.

Common parlance is that we have two, equally probable outcomes and for even the most exact of real world scenarios this is true. If flipped into the air above the table the quarter will either land face up or face down. Since there is no force that would cause the quarter to land one side up with statistical more regularly then the other* and the factors in how the coin are going to land are far outside the ability of the person flipping it to alter, assuming we're talking a good old fashioned honest coin flip and not some kind of slight of hand, we can reasonably assume a coin flip is a fair, real world random event generator with a 50/50 split possible outcome.

But in the realm of pure hypotheticalness we have billions of possible scenarios, practically all of which are so statistically unlikely we can dismiss them when applying a coin flip to any real world scenario. The coin could land perfectly balanced on its side, it could quantum tunnel through the table and land on the floor, etc.

None of these things are likely by any possible definition of the term, so much so that even speaking of the wildest possible outcomes we can safety dismiss them as impossible with intellectual honestly.

Now let's take a bag of 100 marbles, 99 white, and 1 black that a person reaches into and sight unseen picks one. Again here we have two equally possible scenario in a practical sense, a person is going to pick either a white marble or a black one. But the probability of picking a white marble is many times greater then picking a black one.

*And yes I'm aware that due to weight issues on the engraving of some coins they will land on one side statistically more often then other by a small but not insignificant margin, but I'm trying to make a point.
 
If something is possible then it has a probability greater than 0.

That's about it.
 
Probability, in mathematics, is a well defined noun. With the definition comes precision concerning it properties and how it works.

Possibility is not as well defined, and particularly not well defined mathematically. Without it, it's measure is ephemeral and qualitative.
 
On uncountable sets, events of measure 0 do occur (any realisation of a continuous random variable). So saying a "possibility" has probability bigger than 0 is technically false. A better definition of a "possibility" would be any element (or even subset) of the probability space.

But in the end, a possibility is nothing more than a colloquial term.
 
Jorghnassen said:
On uncountable sets, events of measure 0 do occur (any realisation of a continuous random variable). So saying a "possibility" has probability bigger than 0 is technically false. A better definition of a "possibility" would be any element (or even subset) of the probability space.

But in the end, a possibility is nothing more than a colloquial term.
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Perhaps so for some mathematical disciplines, but maybe not for all.

In any case, I don't think that saying that if something has a possibility of 1, it means that it can be or happen, whereas, if it has a possibility of 0 it it can't be or happen.

An example of what I am suggesting...

Newark Mayor Corey Booker this past week rushed into a neighbor's burning building to save her. He found himself in that burning building X with a goal of completely vacating X through an intended doorway Y to hopeful safety in the street.

As Mayor Booker and his neighbor were moving more and more towards the intended Y door to the safety of the street, the probability of their salvation was obviously increasing towards 1. But I submit to you for your response that until they wholly transitioned from being in the burning building to being in the street (where the possibility of burning in the building became 0) the possibility of them burning to death in the burning building remained 1.
 
eijah said:
A probability can be from 0 to 1, but what about a possibility?

That is, is a possibility either 0 or 1? Or can a possibility also be from 0 to 1? Note: I am not talking about conditional probabilities, or am I?
Click to expand...

I would say "possibility" refers to anything with a non-zero probability.

Possibility is not a statistical term, so there is no numerical measure of it (so no, a possibility cannot "also be from 0 to 1").
 
JoeTheJuggler said:
Possibility is not a statistical term, so there is no numerical measure of it (so no, a possibility cannot "also be from 0 to 1").
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I very much agree. E.g., whereas probability to me has the look and feel of a statistical concept, possibility seems to me to be much more an existential one. So how about this: An atheist would say that God has an existential possibility of 0, whereas an agnostic might say that God has a statistical probability of perhaps 0?
 
Surely any event is possible. Some are probable; others are not.

As I was saying to the elephant in my garage. :covereyes
 
eijah said:
A probability can be from 0 to 1, but what about a possibility?

That is, is a possibility either 0 or 1? Or can a possibility also be from 0 to 1? Note: I am not talking about conditional probabilities, or am I?
Click to expand...


Probability is a scalar quantity with a range from zero to one (often expressed as a percentage), while possibility is simply true/false (which can be expressed as one and zero in Boolean algebra).

A probability of zero means impossible (while a probability of one means certain). Anything not impossible is, by definition, possible. Therefore every nonzero probability is a possibility.
 
eijah said:
I very much agree. E.g., whereas probability to me has the look and feel of a statistical concept, possibility seems to me to be much more an existential one.
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That is what everyone would agree: Probability is a defined quantity in statistics. Everyone given the same data and using the same techniques will calculate the same probability (it is an objective measure).

Possibility is a English term for the subjective feeling abut how possible something is.
 
I thought that this was resolved in Pirates of the Caribbean: The Curse of the Black Pearl.
 
Brian-M said:
...possibility is simply true/false (which can be expressed as one and zero in Boolean algebra).
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Hmm, if it were purely true/false, then it wouldn't take qualifiers, like "strongly possible" or "barely possible". There is an element of true/false about it (anything that's not impossible can be described as possible), but it's more complex than that. I wouldn't go so far as to say you're wrong, but I don't think your description tells the whole story.

Natural languages are weird. But fun. :)
 
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