x and y are two real numbers, each of which is uniformly randomly chosen in the interval (1,5).

Determine the probability of each of the following events:

(i) ⌈3*x⌉ + ⌈4*y⌉ = ⌈3*x + 4*y⌉
(ii) ⌈3*x⌉ - ⌈4*y⌉ = ⌈3*x - 4*y⌉
(iii) ⌈3*x⌉ * ⌈4*y⌉ = ⌈12*x*y⌉           
                             
      ⌈3*x⌉              
(iv) --------- = ⌈(3*x)/(4*y)⌉
      ⌈4*y⌉ 

*** ⌈n⌉ denotes ceiling(n), that is, the lowest integer greater than or equal to n.