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Probability Topics: Summary of Formulas

Module by: Kathy Chu. E-mail the author

Based on: Probability Topics: Summary of Formulas by Susan Dean, Barbara Illowsky, Ph.D.

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.

Formula 1: Compliment

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

Formula 2: 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).

If AA and BB are NOT mutually exclusive then 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: 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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