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 prize 2}, 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.