Mutually exclusive

Definition

Mutually exclusive events are events that cannot happen at the same time. If one event occurs, the other cannot.

5 Must Know Facts For Your Next Test

1. If two events are mutually exclusive, their joint probability is zero: $P(A \cap B) = 0$.
2. For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities: $P(A \cup B) = P(A) + P(B)$.
3. Mutually exclusive does not imply independence; in fact, mutually exclusive events are always dependent.
4. An example of mutually exclusive events is rolling a die and getting either an odd number or an even number—not both.
5. Mutually exclusive events help in simplifying complex probability problems by breaking them down into non-overlapping scenarios.

Review Questions

• What is the joint probability of two mutually exclusive events?
• How do you calculate the probability of either of two mutually exclusive events occurring?
• Can two mutually exclusive events be independent? Why or why not?

Related terms

Independent Events:

Two events are independent if the occurrence of one does not affect the occurrence of the other. Mathematically, $P(A \cap B) = P(A) \cdot P(B)$.

Joint Probability:

The probability that two or more events occur simultaneously. For independent events, it is calculated as $P(A \cap B) = P(A) \cdot P(B)$.

Complementary Events: Two complementary events are those which together encompass all possible outcomes. If $A$ is an event, then its complement $A'$ represents all outcomes where $A$ does not occur.