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Ch. 14 - Mendel and the Gene Idea
All textbooksCampbell 12th EditionCh. 14 - Mendel and the Gene IdeaProblem 8
Chapter 14, Problem 8

What is the probability that each of the following pairs of parents will produce the indicated offspring? (Assume independent assortment of all gene pairs.) a. AABBCC×aabbcc→AaBbCc b. AABbCc×AaBbCc→AAbbCC c. AaBbCc×AaBbCc→AaBbCc d. aaBbCC×AABbcc→AaBbCc

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For each cross, use the Punnett square method to determine the probability of the offspring having the desired genotype. Each gene pair (A, B, C) will assort independently according to Mendel's law of independent assortment.
a. AABBCC x aabbcc: Each parent can only produce one type of gamete, AABBCC produces gametes with ABC and aabbcc produces gametes with abc. The offspring AaBbCc results from the combination of these gametes. Since there is only one possible outcome, the probability is 1 (100%).
b. AABbCc x AaBbCc: For the A gene, the possible gametes are A from AABbCc and A or a from AaBbCc. The probability of AA is 1/2. For the B gene, the possible gametes are B or b from both parents, and the probability of Bb is 1/2. For the C gene, the possible gametes are C from AABbCc and C or c from AaBbCc, and the probability of CC is 1/2. Multiply these probabilities: 1/2 * 1/2 * 1/2 = 1/8.
c. AaBbCc x AaBbCc: For each gene, calculate the probability of obtaining the heterozygous condition. For A, the probability of Aa is 1/2, for B, the probability of Bb is 1/2, and for C, the probability of Cc is 1/2. Multiply these probabilities: 1/2 * 1/2 * 1/2 = 1/8.
d. aaBbCC x AABbcc: For the A gene, aa can only pass on a and AA can only pass on A, so Aa is certain, probability is 1. For the B gene, Bb from both parents gives a 1/2 chance of Bb. For the C gene, CC can only pass on C and bc can only pass on c, so Cc is certain, probability is 1. Multiply these probabilities: 1 * 1/2 * 1 = 1/2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It includes concepts such as dominant and recessive alleles, genotype and phenotype, and the laws of segregation and independent assortment, which are crucial for predicting the genetic outcomes of crosses between organisms.
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Punnett Square

A Punnett square is a diagram used to predict the genotypes of offspring from a genetic cross. By organizing the alleles of each parent, it allows for the visualization of all possible combinations of alleles, making it easier to calculate the probabilities of specific genotypes and phenotypes in the offspring.
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Independent Assortment

Independent assortment is one of Mendel's principles stating that alleles for different traits segregate independently of one another during gamete formation. This means that the inheritance of one trait does not affect the inheritance of another, allowing for a variety of genetic combinations in the offspring, which is essential for calculating probabilities in genetic crosses.
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Related Practice
Textbook Question

Flower position, stem length, and seed shape are three characters that Mendel studied. Each is controlled by an independently assorting gene and has dominant and recessive expression as indicated in Table 14.1. If a plant that is heterozygous for all three characters is allowed to self-fertilize, what proportion of the offspring would you expect to be each of the following? (Note: Use the rules of probability instead of a huge Punnett square.) a. homozygous for the three dominant traits b. homozygous for the three recessive traits c. heterozygous for all three characters d. homozygous for axial and tall, heterozygous for seed shape

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Hemochromatosis is an inherited disease caused by a recessive allele. If a woman and her husband, who are both carriers, have three children, what is the probability of each of the following? a. All three children are of normal phenotype. b. One or more of the three children have the disease. c. All three children have the disease. d. At least one child is phenotypically normal.

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Textbook Question

The genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes? a. aabbccdd b. AaBbCcDd c. AABBCCDD d. AaBBccDd e. AaBBCCdd

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Textbook Question

Karen and Steve each have a sibling with sickle-cell disease. Neither Karen nor Steve nor any of their parents have the disease, and none of them have been tested to see if they carry the sickle-cell allele. Based on this incomplete information, calculate the probability that if this couple has a child, the child will have sickle-cell disease.

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Textbook Question

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Textbook Question

In tigers, a recessive allele of a particular gene causes both an absence of fur pigmentation (a white tiger) and a cross-eyed condition. If two phenotypically normal tigers that are heterozygous at this locus are mated, what percentage of their offspring will be cross-eyed? What percentage of cross-eyed tigers will be white?

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