Consider the sample space

where k is a positive integer. We define the events Ai = {(i, y) ∈ Ω ∶ y (i) Using either the multiplicative law or the result of Proposition 2.3, 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 have the same probability, calculate the probability of each event Ai and consequently the probability of the event A.

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= {(x, y) x, y = {1, 2, ..., k}},