You may well be familiar with the words probability and possibility. However, they have different interpretations in mathematics, despite the similar meaning. In this article, you'll learn how they differ from each other, and how it relates to some fundamental concepts in probability.

Probability refers to strict mathematical representation of how likely an event will come out given all the outcomes. When we say an event is improbable, it means the there is zero chance for it to happen, or in real number we will say '0'. It's denoted in fractional form or percentage.

Possibility determines whether an event can happen in real life. Probability is out of question. For instance, it is always true that the sun rises in the east and sets in the west. But we won't call it probable, because everything is certain with zero uncertainties.

Some events can be improbable but possible to happen. For instance, the probability of measuring a length of square root 2 with a ruler is zero. Definitely the length falls within measurable range. However, there are an infinite number of possibilities for the length to take any value between the limits. As a result, it is possible for it to happen.

In conclusion, probability deals with strict sense of numerical representation of likelihood of occurrence, while possibility concerns with whether an event can happen or not in real life dynamics. If we know everything with zero uncertainties, we won't need to bother ourselves with probability. Probability arises from our limited knowledge on subjects. For instance, we can know the outcome of a dice roll, if we know the dynamics that affect the roll.

Now, can you think of an event that is impossible but probable to happen?