Conditional Probabilities Complementary Proof

rbzima
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I'm having trouble seeing how this works out. It's blatantly obvious that this is true, but somehow I can't seem to get anywhere on paper with it to simplify it down to anything. Any help would be greatly appreciated!

P\left(A\right|B)=1-P\left(not A\right|B)
 
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P(A|B) = P(A&B)/P(B)
P(~A|B) = P(~A&B)/P(B)

What is P(A&B) + P(~A&B) = ?
 

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Thread 'Detail of Diagonalization Lemma'

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