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.