I always get confused between the possibility of an event happening vs the probability of an event. I think a lot of people get confused while describing the possibility vs the probability of an event.
Well...after spending a while on this topic, I think I "finally" understood the main difference...
Definition statisticians use to describe the two:
A possibility is something we use to describe an event that may or may not happen. And it might not be always possible to calculate how likely the event is to occur. Possibility is the qualitative characteristic of an event's occurrence. For instance, I may find myself winning a lottery today is a possibility. The probability of an event is the likelihood or chance with which that event could occur or happen. Probability is basically the numerical/quantitative characteristic of the likelihood of an event's occurrence.
Therefore, technically, the possibility of any event is always binary (Yes or a no, 1 or 0). If an event is "possible", how likely will its occurrence be, under a given situation is probability.
Imagine yourself to be playing a game of roll the dice, when your brother rolls a dice, the possibility of the dice showing up number 5 is 'Yes', the possibility of showing up number 10 is 'No'. In a situation where the dice is rolled just once, the probability of it showing up number 5 is 1/6. Well...so the main difference is that possibility is qualitative (likelihood), whereas probability is quantitative. So, next time someone chips in the 'probable' word in his sentence, do ask him what he actually meant...(as we now know means it is likely to occur (especially if it is more likely to happen than not).
PS. I may probably not win the lottery anyway.... (even though it could happen I hope) :(