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I am aware that when some someone says that there is a possibility of something happening, that means that there is a chance that thing might happen. And when they say that there is a probability of something happening, that means that thing is likely to happen. But it gets complicated for me to feel the difference when the words are collocated with the adjective high. For example:

There is a high possibility that he will get the job.

There is a high probability that he will get the job.

I cannot see the difference. Is there any?

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Saying "A high probability" is well understood.

I think most examples I find of "A high possibility" are simply errors. People are using the wrong word. You should not say "A high possibility"; when people do say it, you should understand it to mean the same as "A high probability"

For example:

mufc sources say there is a high possibility the club do not sign anyone in January

This clearly means "A high probability", and this is simply a mistake. (I would also say "will not sign", this is a tweet, and not carefully edited.)

There is an expression "A distinct possibility". This means that something is unlikely, but not very unlikely. Its usually used to emphasise that the probability is not zero:

Last year nobody thought Jack would get promoted, but now there is a distinct possibilty that Jack will not only get promoted, but made Vice-president.

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    +1 for "I think most examples I find of "A high possibility" are simply errors." This is the correct answer.
    – TypeIA
    Feb 28, 2020 at 18:48
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Possible means something can happen, but that's it. It could either be very unlikely or very likely or anywhere in between, the only thing you know is that it isn't impossible (definition).

Probable means it's both possible and has a better chance to occur than to not occur (definition). Something that is probable is always possible, but something that is possible is not always probable.

In everyday speech, people would "highly possible" and "highly probable" interchangeably, but technically "high probability" is the more correct one.

You use "probable" or "improbable" to talk about how likely or unlikely it is for something to happen, and "possible" or "impossible" to talk about whether it can happen at all. So it doesn't really make any sense to say "high possibility" from a literal grammar point of view when you mean to say "high probability". The words are close enough in meaning though that most speakers would not be confused about what you meant.

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You can think of "possibility" as an educated guess and "probability" as the possibility that has been calculated/estimated from previous similar occasions, so it should be more accurately predictable.

Possibility is yes or no: It is or it is not possible.

Probability can be high or low.

So you can say there is or there isn't a possibility and there is a high or low probability.

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