Abox contains the following four slips of paper, each having exactly the same dimensions. win prize 1. win prize 2. win prize 3. 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. to prove pairwise independence, we must first calculate the following probabilities.