Answer all questions with explanation

A random number N of dice is thrown. Let A; be the event that N = i, and assume that P(A;) = 2 ,i> 1. The sum of the scores is S. Find the probability that: (a) N = 2 given S = 4; (b) S = 4 given N is even; (c) N = 2, given that S = 4 and the first die showed 1: (d) the largest number shown by any die is r, where S is unknown