113. 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 ,

, and . 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

, so the three events are not mutually independent.