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Probability Topics: Summary of Formulas

Module by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

Summary: This module provides a review of the probability formulas, including the definitions of independent, complementary, and mutually exclusive events as well as the addition and multiplication rules. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Note: You are viewing an old version of this document. The latest version is available here.

formula 1: Compliment

If AA and A'A' are complements then P(A) + P(A' ) = 1P(A)+P(A' )=1

formula 2: Addition Rule

P(A OR B) = P(A) + P(B) - P(A AND B)P(A OR B)=P(A)+P(B)-P(A AND B)

formula 3: Mutually Exclusive

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

formula 4: Multiplication Rule

  • P(A AND B) = P(B) P(A|B)P(A AND B)=P(B)P(A|B)
  • P(A AND B) = P(A) P(B|A)P(A AND B)=P(A)P(B|A)

formula 5: Independence

If AA and BB are independent then:

  • P(A|B) = P(A)P(A|B)=P(A)
  • P(B|A) = P(B)P(B|A) =P(B)
  • P(A AND B) = P(A) P(B)P(A AND B)=P(A)P(B)

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