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Computing Conditional Probabilities

Computing Conditional Probabilities. Formula for Conditional Probability. Pr{A|B} = Pr{A B} / Pr{B}. The “Given” or Contingent Event. “B” denotes the contingent event. Compute the probability for event B (Pr{B}) separately. . The “Joint” Event.

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Computing Conditional Probabilities

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  1. Computing Conditional Probabilities

  2. Formula for Conditional Probability Pr{A|B} = Pr{AB} / Pr{B}

  3. The “Given” or Contingent Event “B” denotes the contingent event. Compute the probability for event B (Pr{B}) separately.

  4. The “Joint” Event The event “AB” is the event that events A and B occur jointly/together. Compute the probability for AB (Pr{AB}) separately.

  5. The Conditional Probabilty Compute the Conditional Probability Pr{A|B} as Pr{A|B} = Pr{AB} / Pr{B}

  6. A Venn Diagram Pr{U} = 1 Pr{A} = Pr{A}/Pr{U} = Pr{A} Pr{B} = Pr{B}/Pr{U} = Pr{B} AB A B Pr{A|B} = Pr{AB}/Pr{B} U

  7. Notes Think of Pr{A} as being an “unrestricted” probability for A. Then Pr{A|B} is a probability for A that is restricted by B. In Pr{A|B}, A is thought of as not yet observed, with an uncertainty of showing, while B is viewed as being a certainty.

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