Could you explain step by step for the 2nd part of the problem (yellow highlighted---"find posterior probability of Judy is Xx given the information all her N children are Brown eyes, and find probability of her 1st grand child is blue eyes.") how to derive it? I am OK with the 1st part --- Pr(child Xx | child Brown & parents Brown) = 2p/(1+2p) ---- I could get it by breaking down to numerator =Pr (child Xx, child Brown, parent Brown), and denominator = Pr (child Brown, parents Brown) and plug in each probability. But I am getting confused with the 2nd question.

Thank you very much for your help.

Problem Probability calculation for genetics (from Lindley, 1965): suppose that in each individual of a large population there is a pair of genes, each of which can be either x or X, that controls eye color: those with XX have blue eyes, while heterozygotes (those with Xx or XX) and those with XX have brown eyes. The proportion of blue-eyed individuals is p2 and of heterozygotes is 2p(1 p), where 0