Find min cut using randomized algorithm

Given a simple undirected connected graph G, Find a min-cut of G using a randomized algorithm

MY Thoughts –
Select a random edge in G and reduce that edge to a single vertex. And recursively do it
till number of vertices <=2. The number of edges present will be the min-cut.
This is the standard algorithm I found at many places. But I am not sure if this will lead
to exact number of min-cut and the vertices in both set will be the set of two vertices left.