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There is the following famous line in the book, “Life Lessons” co-authored by Elisabeth Kuble-Ross, an expert on death and dying and her colleague, David Kessler,

“We all live with the possibility of death, but the dying live with the probability.”

From this text, it seems “probability” has a larger chance of incidence happening than “possibility.”

Can we translate the level of likelihood of “possibility” and “probability” roughly into percentage of certainty? We say high / low possibility (likelihood). Can’t we say low probability?

P.S.

In Japan, we express possibility (可能性 -kanohsei in Japanese) by percentage, like “There will be 100 (80, 50, 20, 2-3) % possibility of earthquake taking place in Tokyo area in next 30 years,” and we seldom use the word, “蓋然性- gaizensei,” which is a counterpart to English “probability.” “蓋然性- gaizensei,” is a big word, and its usage is limited to academic or scientific writings.

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    There is no rigid definition of either, outside of the science of statistics. Normally "probability" would be interpreted as more probable than "possibility", but there are no number ranges assigned. The only general rule is that saying something is "probable" usually means that it has a better than 50% chance of happening, but that "rule" does not carry over to the word "probability" -- one might say that there's a "5% probability" that X will happen, eg.
    – Hot Licks
    Mar 24, 2015 at 12:26
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    And usually, when discussing percentages or other numerical measures of likelihood, "probability" is used rather than "possibility". But, outside of technical articles, either could be used with a numerical measure and would not be considered to be poor English.
    – Hot Licks
    Mar 24, 2015 at 12:32

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This is a question Statistics professors ask within the first hour of Statistics 101. Possibility vs Probability vs Likelihood. Then the professor would give an interesting story and then he would leave it at a cliff-hanger and say that the rest of story will follow over the course of the next couple of semesters.

In Mathematics, we have the situation of qualitative vs quantitative.

Probability is measurable. It is quantitative.

Possibility is not measurable. Like beautiful, it is a qualitative term.

Likelihood, is the expectation of a probability. Perhaps, if you could understand the concept of acceleration of acceleration, you should be able to visualize the idea of expectation of chances, the probabilities of a probability.

  • what is the probability that the probability is 60%, measured two months prior to election day, of Hillary becoming President?

  • What is the likelihood that the poll figures in May, being the same as those in August? What is the likelihood that the probabilities due to the poll taken in May, accurately reflects Hillary's chances in October?

  • What is the likelihood that the probability due to the 1000 person sample accurately reflects the probable tendencies of this city of 100K?

  • What is the likelihood that when a tree falls in the forest, and only 2% chance that someone would notice it, and then what is the likelihood of that 2% probability being sufficiently insignificant that would allow us to say that there would be no sound observed?

When you ask

  • "What are the possibilities of the space shuttle having a stratospheric accident?" you are asking for the various ways the accident could occur.

  • "What is the probability of the space shuttle having a stratospheric accident?" you are asking for a signature number calculated to tell us how likely such an accident would occur. Such that out of 1000 flights, how many of them would explode in the stratosphere.

  • "Is there possibility of the space shuttle having a stratospheric accident?" you are asking if it is possible, yes/no.

  • "What is the possibility of the space shuttle having a stratospheric accident?" you are asking for that one descriptive possibility.

  • "What are the probabilities of the space shuttle having a stratospheric accident?" you are asking for the various methodologies of calculating the probability to tell us how likely such an accident would occur. Such that out of 1000 flights, how many of them would explode in the stratosphere, comparing various means of analyses.

And please refer to the statistics stack for Likelihood vs Probability.

And the wikipedia explanation.

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Probability is a the term for the branch of statistics dealing with chance and outcome.

Possibility refers to an event that can or cannot happen (binary concept).

Probable is more nuanced mathematics — there is a n% chance of a given outcome, where n = a number between 0-100.

  • Anything that is probable must by definition be possible; However, not everything that is possible is going to be probable.

With that respect you can refer to a low probability rather than a low possibility.

Possibility:

  • The fact or state of being possible: investigating the possibility of life on other planets.

Probability:

  • a measure of how likely it is that some event will occur; a number expressing the ratio of favorable cases to the whole number of cases possible; "the probability that an unbiased coin will fall with the head up to 0.5.

(TFD)

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  • There is a difference between "probable" and "probability", in what they mean in common speech.
    – Hot Licks
    Mar 24, 2015 at 12:28
  • Yes, In common speech probable and possibile are ofter used as synonyms.
    – user66974
    Mar 24, 2015 at 12:35
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    No, I mean if you say "X is probable" that implies that the likelihood is greater than 50%. But if you say that "There is a probability that X will occur" that implies nothing about the likelihood of X.
    – Hot Licks
    Mar 24, 2015 at 12:37
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I think the current answers are missing the meaning of 'probability' being used in the quote in the question, that is, 'the condition of being probable' (Collins), so loosely this means a greater than 50% chance, whereas a 'possibility' loosely means any chance greater than zero.

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    Indeed, consider the negative versions: something which is not probable is more likely than not, i.e. better than 50% chance, to not occur (but it still might), while something which is not possible is certain not to occur at all.
    – talrnu
    Mar 24, 2015 at 14:00
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There indeed seems to be a common speech difference between them that doesn't correlate with the mathematical (or definition) meaning. I feel that words like "likely", "probable", "possible", "not likely" have a decreasing mathematical probability of happening, however there are no defined numbers attached.

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