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Ch. 2 - Transmission Genetics
Chapter 2, Problem 5

Two parents plan to have three children. What is the probability that the children will be two girls and one boy?

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span>Step 1: Determine the probability of having a girl (G) or a boy (B) for each child. Assuming equal probability, P(G) = 0.5 and P(B) = 0.5.</span
span>Step 2: Identify the different combinations of having two girls and one boy. The possible combinations are: GGB, GBG, BGG.</span
span>Step 3: Calculate the probability for each combination. For example, the probability of GGB is P(G) * P(G) * P(B) = 0.5 * 0.5 * 0.5.</span
span>Step 4: Since the order of the children matters, sum the probabilities of all the combinations: P(GGB) + P(GBG) + P(BGG).</span
span>Step 5: The result from Step 4 gives the total probability of having two girls and one boy in any order.</span

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Key Concepts

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

Probability Basics

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In genetics, it often involves calculating the chances of specific outcomes based on known ratios, such as the likelihood of having a boy or a girl. For two parents, the probability of having a boy or a girl is typically considered equal, at 0.5 for each.
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Binomial Distribution

The binomial distribution is a statistical method used to model the number of successes in a fixed number of independent trials, each with the same probability of success. In this context, having a girl can be considered a 'success,' and the distribution helps calculate the probability of having a specific number of girls (successes) in a set number of children (trials).
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Combinatorial Analysis

Combinatorial analysis involves counting the number of ways to arrange or select items from a set. In the context of the question, it helps determine the different arrangements of two girls and one boy among three children. The formula for combinations can be used to find how many unique ways these children can be arranged, which is essential for calculating the overall probability.
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Related Practice
Textbook Question

A pure-breeding tall plant producing oval fruit as described in Problem 2 is crossed to a pure-breeding short plant producing round fruit.

If the F₁ identified in part (a) are crossed to one another, what proportion of the F₂ are expected to be short and produce round fruit? What proportion are expected to be tall and produce round fruit?

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Textbook Question

In mice, black coat color is dominant to white coat color. In the pedigree shown here, mice with a black coat are represented by darkened symbols, and those with white coats are shown as open symbols. Using allele symbols B and b, determine the genotypes for each mouse. 

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Textbook Question

A man, J.B., has a sister with autosomal recessive galactosemia (OMIM 230400), and his partner, S.B., has a brother with galactosemia. Galactosemia is a serious condition caused by an enzyme deficiency that prevents the metabolism of the sugar galactose. Neither J.B. nor S.B. has galactosemia, but they are concerned about the risk that a future child of theirs will have the condition. What is the probability their first child will have galactosemia?

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Textbook Question

A woman, S.R., had a maternal grandfather with hemophilia A (OMIM 306700), an X-linked recessive condition that reduces blood clotting. S.R.'s maternal grandmother and paternal grandparents are free of the condition, as are her partner, his parents, and his grandparents. S.R. has no siblings. She wants to know the chance that a son of hers will have the condition. What is that probability?

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Textbook Question
In a type of parakeet known as a 'budgie,' feather color is controlled by two genes. A yellow pigment is synthesized under the control of a dominant allele Y. Budgies that are homozygous for the recessive y allele do not synthesize yellow pigment. At an independently assorting gene, the dominant allele B directs synthesis of a blue pigment. Recessive homozygotes with the bb genotype do not produce blue pigment. Budgies that produce both yellow and blue pigments have green feathers; those that produce only yellow pigment or only blue pigment have yellow or blue feathers, respectively; and budgies that produce neither pigment are white (albino). List the genotypes for green, yellow, blue, and albino budgies
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Textbook Question
In a type of parakeet known as a 'budgie,' feather color is controlled by two genes. A yellow pigment is synthesized under the control of a dominant allele Y. Budgies that are homozygous for the recessive y allele do not synthesize yellow pigment. At an independently assorting gene, the dominant allele B directs synthesis of a blue pigment. Recessive homozygotes with the bb genotype do not produce blue pigment. Budgies that produce both yellow and blue pigments have green feathers; those that produce only yellow pigment or only blue pigment have yellow or blue feathers, respectively; and budgies that produce neither pigment are white (albino). A cross is made between a pure-breeding green budgie and a pure-breeding albino budgie. What are the genotypes of the parent birds?
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