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mhchen:
Probability: If events A, B, and C are independent. Prove (A or B) and C is independent.
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mhchen:
\[P( (A \cup B)C )= P( (AC) \cup (BC) ) = P(AC) + P(BC) - P( ABC ) \] \[= P(A)P(C) + P(B)P(C) - P(A)P(B)P(C) \] \[= P(C)(P(A) + P(B) - P(A)P(B)) = P(C)P(A \cup B)\]
mhchen:
easy
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