Let A and B be two events, each with positive probability. Prove or disprove each of the following t


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

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

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

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