A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and 3. One slip will be randomly selected. Let A1 ={win prize 1},A2={win prize2}, and A3 ={win prize 3},. Show that A1 and A2 are independent, that A1 and A3 are independent and that A2 and A3 are also independent (this is pairwise independence). However, show that P(A1 ∩ A2 ∩ A3) ≠P(A1).P(A2).P(A3), so the three events are not mutually independent.
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