Out of a set of 3 keys, only 1 opens a certain door. Someone tries the keys successively and let A_{ k} be the event that the right key appears the kth time. Calculate the probability P(A_{ k}):
(i) If the keys tried are not replaced, {k} = 1, 2, 3.
(ii) If the keys tried are replaced, { k} = 1, 2, . . . .