A publishing house offers a new book as standard or luxury edition and with or without a CD. The publisher analyzes the first 1000 orders:

Let \(A(B)\) the random event that a book, randomly choosen from these 1000 , is a luxury one (comes with a CD). (1) Determine the probabilities \(P(A), P(B), P(A \cup B), P(A \cap B), P(A \mid B), P(B \mid A), P(A \cup B \mid \bar{B})\), and \(P(\bar{A} \mid \bar{B})\).
(2) Are the events \(A\) and \(B\) independent?

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luxury edition yes no with CD yes 324 82 no 48 546