Question 1203552
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P(A u B u C) = P( (A u B) u C )
P(A u B u C) = P(A u B) + P(C) - P( (A u B) n C )
P(A u B u C) = P(A) + P(B) - P(A n B) + P(C) - P( (A u B) n C )
P(A u B u C) = P(A) + P(B) - P(A n B) + P(C) - P( (A n C) u (B n C) )
P(A u B u C) = P(A) + P(B) - P(A n B) + P(C) - [ P(A n C) + P(B n C) - P( (A n C) n (B n C) ) ]
P(A u B u C) = P(A) + P(B) - P(A n B) + P(C) - [ P(A n C) + P(B n C) - P( A n B n C ) ]
P(A u B u C) = P(A) + P(B) - P(A n B) + P(C) -  P(A n C) - P(B n C) + P( A n B n C ) 
P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) -  P(A n C) - P(B n C) + P( A n B n C ) 


For more info, search out "inclusion exclusion principle".
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