3. If 1 P[0,1] and 2 P [0,1] are two different probability measures corre- sponding to the same choice of S and P then we can define the distance between and 2 as 2(P)| d(1, 2) = max |(P) (P)| - If S is a finite set and P is the set of all subsets of S then show that 1 d (1,2) = (;) - 2 (5;)| SiS show that d (1, 2) + d (2, 3) d (1, 3).