7 Past Probabilied In this question we review some of the past C870 topics, and look at them probabilisticall y. For the following experiments, i. Dene an appropriate sample space 52. ii. Give the probability function Mm). iii. Compute MEI) given event E]. iv. Compute 113032) given event Eg. (a) Fix a prime p > 2, and uniformly sample twice with replacement from {U,. . . ,p 1} (assume we have two {0, . . . , p l}-sided fair dice and we roll them). Then multiply these two numbers with each other in ( mod p) space. E1 : The resulting product is 0. E2 2 The product is (p l)/2. (b) Make a graph on n vertices by sampling uniformly at random from all possible edges, (assume for each edge we ip a coin and if it is head we include the edge in the graph and otherwise we exclude that edge from the graph). E1 = The graph is complete. E2 2 vertex V] has degree d