What is probability?
BLUF: Probability quantifies uncertainty by assigning numbers (0 to 1) to how likely events are to occur.
A fundamental explanation of what is probability?
The Explanation
Probability quantifies uncertainty by assigning numbers (0 to 1) to how likely events are to occur. It is the mathematical measure of chance: 0 means impossible, 1 means certain. Formally (Kolmogorov axioms), probability is a measure on all possible outcomes of a random experiment. For example, a fair coin flip has P(heads)=0.5, reflecting its symmetry. In practice, probability can be interpreted as a long-run frequency or degree of belief. The Law of Large Numbers says that as trials increase, the observed frequency approaches the theoretical probability. In summary, probability theory provides rules (e.g. for independent events) to calculate the odds of different outcomes under uncertainty.