Exercise 3 Consider the following variation of the min-cut algorithm presented in class. We start with a graph G with n vertices, and we use the randomized min-cut algorithm to contract the graph down to a graph Gk with k = Vn vertices. Next, we make l = n copies of the graph Gk, and run the randomized algorithm independently on each copy of the reduced graph. We output the smallest min-cut set found in all the executions. (a) What is the probability that the reduced graph Gk has the same cut-set value as the original graph G? (b) What is the probability that the algorithm outputs a correct min-cut set? Hint: For a