Statistics for Business: Decision Making and Analysis, 3rd Edition

... outcomes in common, the probability of their union is the sum of the probabilities. This rule is known as the Addition Rule for Disjoint Events.

Rule 3. Addition Rule for Disjoint Events

The probability of a union of disjoint events is the sum of the probabilities. If A and B are disjoint events, then

$$P\left(\text{A}or\text{B}\right)=P\left(\text{A}\right)+P\left(\text{B}\right)$$

The union (shown in green in the Venn diagram) combines A (which was yellow) with B (which was cyan). The Addition Rule for Disjoint Events states the obvious: The area (probability) of the union of A with B is the sum of the two areas.

Caution

Sometimes when speaking, we say the word or to mean one or the other, but not both. “I’m ...