Let p, q, and r be prime natural numbers that are distinct.

(a) What is the probability that n is divisible by p provided that it is divisible by q if n is chosen uniformly at random from {1,2,3,4,..., pqr}?

(b) Are these events, being divisible by p and being divisible by q, independent?

(c) If p=q, how is the part (a) probability going to change?

Please give an explanation for your responses.