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Probability Theory : Independent and Complementary Events Proof

Prove: If P(A)≤P(B) then P(A|C)≤P(B|C). Show that if A,B,C are independent the events A-bar, B, and C-bar are independent.
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An independent and complementary events proof is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.