Problem 2.68 Consider the sample space consisting of the 9 ordered triples: (a,a,a),

(b,

b. b),

(c,

c, c),

(a,

b, c),

(a,

c, b),

(b,

a, c),

(b,

c, a),

(c,

a, b),

(c,

b, a) equipped with equally likely probability measure. Let Ak denote the event that the kth coordinate is occupied by

a. == Thus, A = {

(a,

a, a),

(a,

b, c),

(a,

c, b)}, etc. Show that the events A1, A2, A3 are:

(a) pairwise independent, i.e., P(A; n A) = P(A)P(A), but

(b) not mutually independent, i.e., P(An An As) + P(A)P(A2)P(A3).