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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. 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

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  1. Mutually Exclusive, Independent, Dependent, and Complementary Events Sections 4.5, 4.6, 4.7

  2. Mutually Exclusive Events • Events that cannot occur together. • Example: Even or Odd number on die.

  3. NOT Mutually Exclusive • Mutually Nonexclusive. • Example: Even or < 5

  4. Example

  5. 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.

  6. Example: Independent or Dependent? • Event D and Event A

  7. Example: Independent or Dependent? • Event “Female” and Event “in favor”

  8. 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.

  9. 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.

  10. Example: Smoker/Nonsmoker

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