The color of a person\'s eyes is determined by a single pair ofgenes. If they ar
ID: 2953356 • Letter: T
Question
The color of a person's eyes is determined by a single pair ofgenes. If they are both blue-eyed genes, then the person will haveblue eyes; if they are both brown-eyed genes, then the person willhave brown eyes; and if one of them is a blue-eyed gene and theother a brown-eyed gene, then the person will have brown eyes.(Because of the latter fact, we say that te brown-eyed gene isdominant over the blue-eyed gene.) A newborn child independentlyreceives one eye gene from each of its parents, and the gene itreceives from a parent is equally likely to be either of the twoeye genes of that parent. Suppose that Smith and bot of his parentshave brown eyes, but Smith's sister has blue eyes. What is the probability that Smith possesses a blue-eyedgene? Suppose that Smith's wife has blue eyes. What is theprobability that their first child will have blue eyes? If their first child has brown eyes, what is the probabilitythat their next child will also have brown eyes? The color of a person's eyes is determined by a single pair ofgenes. If they are both blue-eyed genes, then the person will haveblue eyes; if they are both brown-eyed genes, then the person willhave brown eyes; and if one of them is a blue-eyed gene and theother a brown-eyed gene, then the person will have brown eyes.(Because of the latter fact, we say that te brown-eyed gene isdominant over the blue-eyed gene.) A newborn child independentlyreceives one eye gene from each of its parents, and the gene itreceives from a parent is equally likely to be either of the twoeye genes of that parent. Suppose that Smith and bot of his parentshave brown eyes, but Smith's sister has blue eyes. What is the probability that Smith possesses a blue-eyedgene? Suppose that Smith's wife has blue eyes. What is theprobability that their first child will have blue eyes? If their first child has brown eyes, what is the probabilitythat their next child will also have brown eyes?Explanation / Answer
Because Smith's sister has blue eyes, both parents must have blueeye gene. Because both parents have brown eyes, they eachhave one blue eye gene Smith has Brown eyes. Therefore the possible equally likelystates are BrBr, BrBl, BlBr. He has a 2/3 chance of having aBlue eye gene. The probability that Smith's first born has blue eyes is prob thatsmith donates a blue eye gene -- ie 2/3 * 1/2 = 1/3 If the first born has brown eyes, (Br,Br) 1/3 + (BrBl) 1/6 + (BlBr) 1/6 The prob that the next also has brown eyes is 2/3