1. A number is selected at random from the set {1, 2,..., 1200). All numbers in the set are equally likely to be chosen. What is the probability that the randomly selected number is not divisible by 4, 7 or 9? 2. Suppose that we have a sample space S with event space F and probability function P. Let BEF be such that P(B)>0. Prove that the conditional probability function Q(A) = P(A|B) is a proper probability function. This means you need to state the new sample space and new event space associated with Q, prove that the new event space satisfies the required properties of an event space, and prove that Q satisfies the required properties of a probability function on that new event space.