Solutions Calculus

Let E, F, and G be three events, each with positive probability. Prove or disprove that P(E|F)=P(E|

Question: Let E, F, and G be three events, each with positive probability. Prove or disprove that $P(E|F)=P(E|FG)P(G|F)+P(E|F{{G}^{C}})P({{G}^{C}}|F)$ .

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