Question

An urn contains N balls each labeled with a unique number 1, 2, ..., N. M of these balls are colored yellow and the remaining N-M are blue, 0<=M<=N. These facts represent our state of knowledge, or information A. Yi $\equiv$ yellow ball on ith draw and Bi $\equiv$ blue ball on ith draw. For the ith draw it must be that p[Yi | A] + p[Bi | A] = 1. Find the probability for drawing a yellow ball on the first m <= M consecutive draws. And find the probability for drawing exactly m $\leq$ M red balls in n $\leq$ N draws, regardless of order. And find the probability of drawing a yellow ball on the first two draws, without replacement, i.e., find p[Y1Y2 | A]. Show your steps and explain in words.

Answer 1