5. Consider an urn containing N balls each labeled with a unique number 1,2,..., N. M of these balls are colored red and the remaining N-M are white, 0 MN. Understand that these facts represents our state of knowledge, or information I. Let R = red ball on the ith draw and W = white ball on the ith draw. According to our knowledge of the composition of the urn, only red or white can be drawn, thus, for the ith draw it must be that p[R;|I] + p[W;|I] = 1. a) Find the probability of drawing and red or white ball on the first draw, i.e. p[R|I]? and P[Wil!] [2 points] b) Find the probability of drawing a red ball on the first two draws, assuming you are sampling without replacement, i.e. find p[RR[I] [3 points] c) Following this logic find the probability for drawing a red ball on the first m M consecutive draws. Show your logic. [5 points] d) Find the probability for drawing exactly m M red balls in n N draws, regard- less of order. [5 points]