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Traditional definition of independence says that events A and B are independent if and only if P(A...

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Question

Basic Math

Traditional definition of independence says that events A and Bare
independent if and only if P(A n B)=P(A)×P(B). Show that P(A nB)=P(A)×P(B) if
and only if
a. P(A n B’) = P(A) × P(B’)b. P(A’ n B’) = P(A’) × P(B’)
You may use these without proof in your solutions:
o P(A n B’) = P(A) – P(A n B). [This can be proven by first showingthat
(A ∩ B ′ ) ∪̇ (A ∩ B) = A and using the Addition Rule.]
o P(A n B) = 1 – P(A’ n B’). [This can be proven by noting thatunder de
Morgan’s Law, (A n B)’ = A’ n B’.]

Answer & Explanation Solved by verified expert
3.9 Ratings (479 Votes)
Solution Backup Theory PA B PA PA B 1 PA B 1 PA B 2 PA B PA PB PA B 2b Now to work out the solution Part 1 subpart a Given PA B PA x PB 3a to show PA B PA x PB 3b Now vide 1 LHS    See Answer
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