mutually exclusive

(adjective)

describing multiple events or states of being such that the occurrence of any one implies the non-occurrence of all the others

Related Terms

Examples of mutually exclusive in the following topics:

  • Complementary Events

    • The event $A$ and its complement $[\text{not}\ A]$ are mutually exclusive and exhaustive, meaning that if one occurs, the other does not, and that both groups cover all possibilities.
    • Generally, there is only one event $B$ such that $A$ and $B$ are both mutually exclusive and exhaustive; that event is the complement of $A$ .
    • There are no other possibilities (exhaustive), and both events cannot occur at the same time (mutually exclusive).
    • Since we can only either chose blue or red (exhaustive) and we cannot choose both at the same time (mutually exclusive), choosing blue and choosing red are complementary events, and $P(\text{blue}) + P(\text{red}) = 1$.
    • Clearly, a number cannot be both prime and composite, so that takes care of the mutually exclusive property.

  • Student Learning Outcomes

    • Determine whether two events are mutually exclusive and whether two events are independent.

  • The Addition Rule

    • If A and B are mutually exclusive, then P(A AND B) = 0.
    • Are being an advanced swimmer and an intermediate swimmer mutually exclusive?
    • P(advanced AND intermediate) = 0, so these are mutually exclusive events.
    • For B and N to be mutually exclusive, P(B AND N) must be 0.

  • Summary of Formulas

    • If A and B are mutually exclusive then P(A AND B) = 0 ; so P(A OR B) = P(A) + P(B).

  • Practice 2: Calculating Probabilities

    • Students will determine whether two events are mutually exclusive or whether two events are independent.
    • Are L and C mutually exclusive events?

  • Mutually Exclusive Events

    • Therefore, A and B are not mutually exclusive.
    • Therefore, A and C are mutually exclusive.
    • B and C are mutually exclusive.
    • Therefore, C and D are mutually exclusive events.
    • Are C and E mutually exclusive events?

  • Disjoint or mutually exclusive outcomes

    • Two outcomes are called disjoint or mutually exclusive if they cannot both happen.
    • The terms disjoint and mutually exclusive are equivalent and interchangeable.

  • Homework

    • Are A and B mutually exclusive events?
    • E and F mutually exclusive events.
    • U and V are mutually exclusive events.
    • G and H are mutually exclusive events.
    • Are G and F mutually exclusive events?

  • Independent Events

  • Review