What fraction of all combinations is guaranteed to be deadlock free?
Let's assume for simplicity that A and B take 5 seconds to request for the next resource and B starts requesting for resources 1 second after A's request.


If A requests for 1 first and B requests for either 2/3 first, it will create a deadlock. This happens because when A requests for either 2/3 it will be blocked and B will be blocked when it requests for 1. So both processes will block each other and in turn will be blocked by each other.
If A and B both request for 1, then A wins out and B will be blocked. So there will be no deadlock.


So the entire problems rests on B's choices. Therefore $\frac{1}{3}$rd of the cases will be deadlock free.