Consider the infinite countable sample space = {0, 1, 2,}. On this space, assume that the probabilities of the elementary events {i}, for i

Consider the infinite countable sample space Ω = {0, 1, 2,…}. On this space, assume that the probabilities of the elementary events {i}, for i = 0, 1,…, are given by

(i) Show that the probability that the outcome of the experiment is at least k, for k = 1, 2,…, is given by (3∕4)k.
(ii) What is the probability that we get an outcome less than k for k = 1, 2,…?

3' P({i}) 4'+1' i = 0, 1, 2,....