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You are watching: A couple has two female children. what is the probability that their next child will be male?

Griffiths AJF, Gelbart WM, müller JH, et al. Contemporary Genetic Analysis. Brand-new York: W. H. Freeman; 1999.

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2. Phenylketonuria (PKU) is a rarely autosomal recessive disease. A couple wants to have actually childrenbut consults a genetic counselor since the man has actually a sister through PKU and the woman has actually abrother with PKU. There room no various other known situations in their families. They ask the geneticcounselor to determine the probability the their an initial child will have PKU. What is thisprobability?

What can we deduce? If us let the allele causing the PKU phenotype be p andthe corresponding normal allele it is in P, climate the man’s sister and woman’s brothermust have actually been p/p. In stimulate to develop these impacted individuals, every fourgrandparents must have been heterozygous common (P/p). The pedigree have the right to besummarized as follows:


The only way the couple can have actually a son with PKU is if both of them are heterozygotes (it isobvious the they themselves carry out not have the disease). Both the grandparental matings aresimple monohybrid the cross (P/p × P/p) expected to produceprogeny in the adhering to proportions:


We know that the man and the woman space normal, so for each of lock the probability of gift aheterozygote is 2/3, since within the regular P/– class, 2/3 areP/p and 1/3 are P/P. Therefore, making use of the product rule, theprobability that both the man and the woman being heterozygotes is 2/3 × 2/3 = 4/9. If lock areboth heterozygous, then one-quarter the their kids would have actually PKU, so the probability thattheir an initial child will have PKU is 1/4, and the probability of their being heterozygousand of their first child having PKU is 4/9 × 1/4 = 4/36 = 1/9, which is theanswer to the question.

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