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Ch. 2 - Transmission Genetics
Sanders - Genetic Analysis: An Integrated Approach 3rd Edition
Sanders3rd EditionGenetic Analysis: An Integrated ApproachISBN: 9780135564172Not the one you use?Change textbook
Chapter 2, Problem 34

A man and a woman are each heterozygous carriers of an autosomal recessive mutation of a disorder that is fatal in infancy. They both want to have multiple children, but they are concerned about the risk of the disorder appearing in one or more of their children. In separate calculations, determine the probabilities of the couple having five children with 0, 1, 2, 3, 4, and all 5 children being affected by the disorder.

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span>Step 1: Identify the genotypes of the parents. Since both are heterozygous carriers, their genotypes are Aa, where 'A' is the normal allele and 'a' is the recessive allele causing the disorder.
span>Step 2: Determine the possible genotypes of their children using a Punnett square. The possible genotypes are AA, Aa, Aa, and aa, with probabilities of 1/4, 1/2, 1/2, and 1/4, respectively. Only 'aa' results in the disorder.
span>Step 3: Calculate the probability of a single child being affected by the disorder. This is the probability of the child having the 'aa' genotype, which is 1/4.
span>Step 4: Use the binomial probability formula to calculate the probability of having exactly k affected children out of 5. The formula is P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k)), where n is the total number of children, k is the number of affected children, p is the probability of a child being affected, and C(n, k) is the binomial coefficient.
span>Step 5: Apply the formula for each case: 0, 1, 2, 3, 4, and 5 affected children, using n = 5 and p = 1/4. Calculate C(5, k) for each k and substitute into the formula to find the probabilities.

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Key Concepts

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

Autosomal Recessive Inheritance

Autosomal recessive inheritance occurs when a disorder is caused by mutations in genes located on autosomes, and two copies of the mutated gene (one from each parent) are necessary for the disorder to manifest. In this case, both parents are heterozygous carriers, meaning they each have one normal allele and one mutated allele. Their children have a 25% chance of inheriting two mutated alleles and thus being affected by the disorder.
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Autosomal Pedigrees

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two individuals. For this couple, a 2x2 Punnett square can illustrate the possible combinations of alleles their children might inherit. The results show that there is a 25% probability of a child being affected by the disorder, a 50% chance of being a carrier, and a 25% chance of being unaffected.
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Binomial Probability

Binomial probability is a statistical method used to determine the likelihood of a specific number of successes in a fixed number of trials, given a constant probability of success. In this scenario, the couple can use the binomial formula to calculate the probabilities of having 0, 1, 2, 3, 4, or 5 affected children out of 5 total, using the probability of 0.25 for each child being affected.
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Related Practice
Textbook Question

An organism having the genotype AaBbCcDdEe is self-fertilized. Assuming the five genes assort independently, determine the following proportions:


Progeny that are expected to have a phenotype identical to that of the parent.

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Textbook Question

An organism having the genotype AaBbCcDdEe is self-fertilized. Assuming the five genes assort independently, determine the following proportions:


Gametes that are expected to be ABcde.

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Textbook Question

An organism having the genotype AaBbCcDdEe is self-fertilized. Assuming the five genes assort independently, determine the following proportions:


Progeny that are expected to have the genotype AabbCcDdE–

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Textbook Question

For a single dice roll, there is a 1/6 chance that any particular number will appear. For a pair of dice, each specific combination of numbers has a probability of 1/36 occurring. Most total values of two dice can occur more than one way. As a test of random probability theory, a student decides to roll a pair of six-sided dice 300 times and tabulate the results. She tabulates the number of times each different total value of the two dice occurs. Her results are the following:

Total Value of Two Dice      Number of Times Rolled
               2                                          7
               3                                         11
               4                                         23
               5                                         36
               6                                         42
               7                                         53
               8                                         40
               9                                         38
              10                                        30
              11                                        12
              12                                         8
           TOTAL                                   300

The student tells you that her results fail to prove that random chance is the explanation for the outcome of this experiment. Is she correct or incorrect? Support your answer.

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Textbook Question

You have four guinea pigs for a genetic study. One male and one female are from a strain that is pure-breeding for short brown fur. A second male and female are from a strain that is pure-breeding for long white fur. You are asked to perform two different experiments to test the proposal that short fur is dominant to long fur and that brown is dominant to white. You may use any of the four original pure-breeding guinea pigs or any of their offspring in experimental matings. Design two different experiments (crossing different animals and using different combinations of phenotypes) to test the dominance relationships of alleles for fur length and color, and make predictions for each cross based on the proposed relationships. Anticipate that the litter size will be 12 for each mating and that female guinea pigs can produce three litters in their lifetime.

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Textbook Question

Galactosemia is an autosomal recessive disorder caused by the inability to metabolize galactose, a component of the lactose found in mammalian milk. Galactosemia can be partially managed by eliminating dietary intake of lactose and galactose. Amanda is healthy, as are her parents, but her brother Alonzo has galactosemia. Brice has a similar family history. He and his parents are healthy, but his sister Brianna has galactosemia. Amanda and Brice are planning a family and seek genetic counseling. Based on the information provided, complete the following activities and answer the questions.

Draw a pedigree that includes Amanda, Brice, and their siblings and parents. Identify the genotype of each person, using G and g to represent the dominant and recessive alleles, respectively.

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