Prove or show..is it possible

**statman101** · September 20th 2009, 03:03 PM

That for any three events A,B, and C with P(C)>0,
P(A U B|C) = P(A|C) + P(B|C) - P(Aint.B|C)

**Plato** · September 20th 2009, 03:23 PM

Notice that $P\left[ {\left( {A \cap C} \right) \cup \left( {B \cap C} \right)} \right] = P\left[ {\left( {A \cap C} \right)} \right] + P\left[ {\left( {B \cap C} \right)} \right] - P\left[ {\left( {A \cap B \cap C} \right)} \right]$

Moreover, $P\left[ {\left( {A \cap B \cap C} \right)} \right] = P\left[ {\left( {A \cap B} \right)|C} \right]P(C)$

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