The color of a persons eyes is determined by a singlepair

Chapter 3, Problem 3.60

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The color of a persons eyes is determined by a singlepair of genes. If they are both blue-eyed genes,then the person will have blue eyes; if they areboth brown-eyed genes, then the person will havebrown eyes; and if one of them is a blue-eyed geneand the other a brown-eyed gene, then the personwill have brown eyes. (Because of the latterfact, we say that the brown-eyed gene is dominantover the blue-eyed one.) A newborn child independentlyreceives one eye gene from each of itsparents, and the gene it receives from a parent isequally likely to be either of the two eye genes ofthat parent. Suppose that Smith and both of hisparents have brown eyes, but Smiths sister hasblue eyes.(a) What is the probability that Smith possesses ablue-eyed gene?(b) Suppose that Smiths wife has blue eyes. Whatis the probability that their first child will haveblue eyes?(c) If their first child has brown eyes, what is theprobability that their next child will also havebrown eyes?