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Chapter 3: Problem 13

Albinism, lack of pigmentation in humans, results from an autosomal recessive gene (a). Two parents with normal pigmentation have an albino child. (a) What is the probability that their next child will be albino? (b) What is the probability that their next child will be an albino girl? (c) What is the probability that their next three children will be albino?

Short Answer

Expert verified
Answer: The probability of their next child being an albino girl is 12.5%.

Step by step solution

01

(Identify genotypes)

Since both parents have normal pigmentation but have produced an albino child, we can determine that both of them are heterozygous carriers of the albinism gene. This means their genotypes are Aa x Aa, where "A" represents the dominant allele for normal pigmentation and "a" is the recessive allele for albinism.
02

(Create a Punnett square)

To determine the probability of different genotypes for the next child, we can use a Punnett square to list all possible combinations of alleles from both parents. The Punnett square is as follows: | A | a ----------- A | AA | Aa ----------- a | Aa | aa
03

(a) Calculate the probability of an albino child)

The probability of an albino child is determined by the probability of inheriting the recessive "aa" genotype. According to the Punnett square, there is one "aa" genotype out of four possible genotypes, so the probability of their next child being albino is 1/4 or 25%.
04

(b) Calculate the probability of an albino girl)

To determine the probability of the next child being an albino girl, we first need to consider the gender probability. The probability of having a girl is 1/2 or 50%. Therefore, the probability of an albino girl is the product of the probabilities of being a girl and being albino: (1/2) * (1/4) = 1/8 or 12.5%
05

(c) Calculate the probability of three consecutive albino children)

To determine the probability of their next three children all being albino, we need to calculate the probability of three consecutive albino children. This probability can be calculated by taking the probability of one albino child and raising it to the power of 3 (because there are three independent events): (1/4) * (1/4) * (1/4) = (1/4)^3 = 1/64 or 1.56%

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