Hello I need help with this part of the assignment please , thank you

Problem(12) (a) (5 points) Show that if 2" - 1 is prime, then n is prime. [Hint. Use the identity 20b - 1 = (20 - 1) . (20(6-1) + 20(6-2) + .. . 20 + 1).] (b) (3 points) Use the result in (a) to identify which of the following is (are) NOT prime? 211 - 1 , 213 - 1 , 215 - 1 , 217 - 1 , 219 - 1 , 221 - 1 . Problem(13) (10 points) Consider a random experiment of throwing two fair dice together. (a) Describe the sample space S and assign probabilities to each sample point in S. (b) Let X be the random variable that corresponds to the sum of the two dice. What are the values that the random variable X takes? (c) Find the following: P(X = 5). P(X