Let A1, A2,, An be a finite collection of events on a sample space such that

Let A1, A2,…, An be a finite collection of events on a sample space Ω such that A1 ∪ A2 ∪ · · · ∪ An = Ω and the Ai’s are pairwise disjoint. If it is known that P(Ai) = 3P(Ai+1) for i = 1, 2,…, n − 1, find P(A3) and P(A5) (assuming n ≥ 5).