In probability, disjoint events are mutually exclusive, meaning that if one of the possible disjoint events occurs, the other cannot occur. For example, when a driver reaches an intersection, she may turn left or right, or go straight, but may not turn and go straight. Turning and driving straight are therefore disjoint events.
Mathematicians illustrate the principles of disjoint probability with the equation P(A and B) = 0, with P representing probability and A and B representing two disjoint events. In this equation, the probability of A and B occurring is zero. The probability of A or B occurring in disjoint events is simply the sum of the probability of A and B.
This principle is clear in the example with the driver approaching an intersection. The probability of the driver turning left, turning right or going straight is one-third for each case, but the probability of turning left or right is two-thirds, which is the sum of those two probabilities.
The opposite of a disjoint event is an independent event. With independent events, the probability of one event has no effect on the probability of the other. For example, if two drivers approach an intersection and one turns left, the probability of the other driver turning left is not affected.