Consider now the sample space = {(x, y, z) x, y, z {1, 2,,

Consider now the sample space

Ω = {(x, y, z) ∶ x, y, z ∈ {1, 2,…, k}},

where k is a positive integer. We define the events Ai = {(i, y, z) ∈ Ω ∶ y (i) Arguing as in part (i) of the previous exercise, find the number of elements of Ω.
(ii) Verify that the events Ai are pairwise disjoint and that

(iii) Assuming that all elements of Ω are equiprobable, calculate the probability of each event Ai and, hence, find the probability of the event A.

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A: k A = = UA; i=2