The union of two events E₁ and E₂, denoted by E₁ ∪ E₂ is the event consisting of all outcomes that are either in E₁ or in E₂ or in both E₁ and E₂.

If two events E₁ and E₂ are associated with “OR”, then it means that either E₁ or E₂ or both E₁ and E₂. The union symbol “∪” is used to represent “OR” in probability. Thus, the events E₁ or E₂ denotes

E₁ ∪ E₂.

If two events E₁ and E₂ are not mutually exclusive, then they share outcomes in common. The overlap of the two sets is their intersection, that is, E₁ ∩ E₂. The probability that E₁ or E₂ will happen is the sum of the probability of each event, minus the probability of the overlapping.

Addition Rule of Probability

We can easily calculate probabilities of compound events by making use of the addition rule stated below.

If two events, E₁ and E₂, are non-mutually exclusive, there is some overlapping between these events. The probability that E₁ or E₂ will happen is the sum of the probability of each event, minus the probability of the overlapping.