Properties of probabilities

Properties of probabilities



The probability axioms imply many interesting properties.

The complement of set A is the set of all elements that do not belong to set A. So a set together with its complement make up the entire sample space.

The complement of the entire sample space consists of all elements that do not belong to the sample space. But since the sample space is supposed to contain all possible elements, its complement is just the empty set. There is 0 probability that the outcome of the experiment would lie in the empty set.

If the sets A1 up to Ak are disjoint then the probability of the union of those sets is going to be equal to the sum of their individual probabilities.