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Mutually Exclusive, Independent, Dependent, and Complementary Events. Sections 4.5, 4.6, 4.7. Mutually Exclusive Events. Events that cannot occur together. Example: Even or Odd number on die. NOT Mutually Exclusive. Mutually Nonexclusive . Example: Even or < 5. Example.

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mutually exclusive independent dependent and complementary events

Mutually Exclusive, Independent, Dependent, and Complementary Events

Sections 4.5, 4.6, 4.7

mutually exclusive events
Mutually Exclusive Events
  • Events that cannot occur together.
  • Example: Even or Odd number on die.
not mutually exclusive
NOT Mutually Exclusive
  • Mutually Nonexclusive.
  • Example: Even or < 5
independent vs dependent events
Independent vs. Dependent Events
  • Two events are Independent if the occurrence of one does not change the probability of the other.
  • P(A | B ) = P(A) or P(B | A) = P(B)
  • If P(A | B ) ≠ P(A) or P(B | A) ≠ P(B), then the events are Dependent.
example independent or dependent1
Example: Independent or Dependent?
  • Event “Female” and Event “in favor”
observations
Observations:
  • Two events are either Mutually Exclusive or Independent.
    • Mutually exclusive events are always dependent.
    • Independent events are never mutually exclusive.
  • Dependent events may or may not be mutually exclusive.
complementary events
Complementary Events
  • The complement of event A is the event that includes all outcomes that are not A.
  • Notation A and A.
  • Complementary Events are always mutually exclusive.
  • Two complementary events must be all the outcomes of an experiment.
  • P(A) + P(A) = 1.