Math Solutions

[See Steps] Let A and B be two events, each with positive probability. Prove or disprove each of the following three statements: P(A|B)+P(A^c|B)=1

Question: Let A and B be two events, each with positive probability. Prove or disprove each of the following three statements:

  1. \[P(A|B)+P({{A}^{c}}|B)=1\]
  2. \[P(A|B)+P(A|{{B}^{c}})=1\]

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