please solve all parts of the question on page by handwriting

and please write a paragraph in the end how did you solved the project so i can understand the steps

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 = \\/1_z vertices. Next, we make I = \\/7_7, 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 G k 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