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Consider three independently assorting gene pairs, \(A / a, B / b,\) and \(C / c,\) where each demonstrates typical dominance \((A-, B-, C-)\) and recessiveness \((a a, b b, c c) .\) What is the probability of obtaining an offspring that is \(A A B b C c\) from parents that are \(A a B b C C\) and \(A A B b C c ?\)

Short Answer

Expert verified
Answer: The probability of obtaining an offspring with the genotype \(AABbCc\) from these parents is 0.

Step by step solution

01

Find the probability of obtaining an \(AA\) allele from the parents

To get an \(AA\) allele, the offspring has to inherit the dominant allele \(A\) from both parents. The first parent has a genotype of \(Aa\), which means the probability of passing on the \(A\) allele is 1/2 (since there's 1 dominant allele and 2 alleles in total for this gene pair). The second parent has a genotype of \(AA\), which means the probability of passing on the \(A\) allele is 1 (since there are 2 dominant alleles and 2 alleles in total for this gene pair). Multiply the probabilities from each parent to get the probability of obtaining an \(AA\) offspring: \(P(AA) = \frac{1}{2} * 1 = \frac{1}{2}\)
02

Find the probability of obtaining a \(Bb\) allele from the parents

To get a \(Bb\) allele, the offspring has to inherit one dominant allele \(B\) and one recessive allele \(b\) from the parents. Both parents have genotypes of \(Bb\) for this gene pair, which means the probability of passing on the \(B\) allele is 1/2, and the probability of passing on the \(b\) allele is also 1/2. To obtain a \(Bb\) offspring, it can either inherit \(B\) from the first parent and \(b\) from the second, or inherit \(b\) from the first parent and \(B\) from the second. Therefore, we have to add the probabilities of these two cases: \(P(Bb) = (\frac{1}{2} * \frac{1}{2}) + (\frac{1}{2} * \frac{1}{2}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}\)
03

Find the probability of obtaining a \(Cc\) allele from the parents

To get a \(Cc\) allele, the offspring has to inherit the recessive allele \(c\) from both parents. The first parent has a genotype of \(CC\) and the second parent has a genotype of \(Cc\). Since the first parent does not have a \(c\) allele, the probability of obtaining a \(Cc\) offspring from these parents is 0. \(P(Cc) = 0\)
04

Calculate the probability of obtaining an \(AABbCc\) offspring from the parents

To find the probability of obtaining an \(AABbCc\) offspring, we need to multiply the probabilities we found in steps 1-3: \(P(AABbCc) = P(AA) * P(Bb) * P(Cc) = \frac{1}{2} * \frac{1}{2} * 0 = 0\) The probability of obtaining an offspring with the genotype \(AABbCc\) from these parents is 0.

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Most popular questions from this chapter

In a cross between a black and a white guinea pig, all members of the \(F_{1}\) generation are black. The \(F_{2}\) generation is made up of approximately \(3 / 4\) black and \(1 / 4\) white guinea pigs. Diagram this cross, and show the genotypes and phenotypes.

Among dogs, short hair is dominant to long hair and dark coat color is dominant to white (albino) coat color. Assume that these two coat traits are caused by independently segregating gene pairs. For each of the crosses given below, write the most probable genotype (or genotypes if more than one answer is possible) for the parents. It is important that you select a realistic symbol set and define each symbol below. (a) dark, short \(\times\) dark, long \(26 \quad 24 \quad 0\) (b) albino, short \(\times\) albino, short \(0 \quad 0 \quad 102 \quad 33\) (c) dark, short \(\times\) albino, short \(16 \quad 0 \quad 16\) (d) dark, short \(\times\) dark, short \(175 \quad 67 \quad 61 \quad 21\) Assume that for cross (d), you were interested in determining whether fur color follows a 3: 1 ratio. Set up (but do not complete the calculations) a Chi-square test for these data [fur color in cross (d)].

Two true-breeding pea plants are crossed. One parent is round, terminal, violet, constricted, while the other expresses the contrasting phenotypes of wrinkled, axial, white, full. The four pairs of contrasting traits are controlled by four genes, each located on a separate chromosome. In the \(F_{1}\) generation, only round, axial, violet, and full are expressed. In the \(\mathrm{F}_{2}\) generation, all possible combinations of these traits are expressed in ratios consistent with Mendelian inheritance. (a) What conclusion can you draw about the inheritance of these traits based on the \(\mathrm{F}_{1}\) results? (b) Which phenotype appears most frequently in the \(\mathrm{F}_{2}\) results? Write a mathematical expression that predicts the frequency of occurrence of this phenotype. (c) Which \(\mathrm{F}_{2}\) phenotype is expected to occur least frequently? Write a mathematical expression that predicts this frequency. (d) How often is either \(P_{1}\) phenotype likely to occur in the \(F_{2}\) generation? (e) If the \(F_{1}\) plant is testcrossed, how many different phenotypes will be produced?

Two organisms, \(A A B B C C D D E E\) and aabbccddee, are mated to produce an \(\mathrm{F}_{1}\) that is self-fertilized. If the capital letters represent dominant, independently assorting alleles: (a) How many different genotypes will occur in the \(\mathrm{F}_{2}\) ? (b) What proportion of the \(\mathrm{F}_{2}\) genotypes will be recessive for all five loci? (c) Would you change your answers to (a) and/or (b) if the initial cross occurred between \(A A b b C C d d e e \times a a B B c c D D E E\) parents? (d) Would you change your answers to (a) and/or (b) if the initial cross occurred between \(A A B B C C D D E E \times\)aabbccddEE parents?

Mendel crossed peas having round seeds and yellow cotyledons with peas having wrinkled seeds and green cotyledons. All the \(\mathrm{F}_{1}\) plants had round seeds with yellow cotyledons. Diagram this cross through the \(\mathrm{F}_{2}\) generation, using both the Punnett square and forked-line methods.

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