Ch. 4 - Probability

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 4 - Probability

Problem 4.1.28a

Chapter 4, Problem 4.1.28a

In Exercises 21-28, find the probability and answer the questions.

X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?

Verified step by step guidance

Step 1: Understand the genetic inheritance. Each parent contributes one chromosome to the child. The father contributes either an X or a Y chromosome, while the mother contributes one of her two X chromosomes.

Step 2: Identify the genetic makeup of the parents. The father has a defective x chromosome (xY), and the mother has two good X chromosomes (XX).

Step 3: Determine the possible combinations of chromosomes for a son. A son inherits the Y chromosome from the father and one of the X chromosomes from the mother. The possible combinations are YX and Yx.

Step 4: Analyze the combinations. A son with the YX combination will not have the disease because the X chromosome from the mother is not defective. A son with the Yx combination will have the disease because the X chromosome from the mother is defective.

Step 5: Calculate the probability. Since the mother has two X chromosomes and each is equally likely to be passed on, the probability of the son inheriting the defective x chromosome is 1/2. Therefore, the probability that the son will inherit the disease is 1/2.

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Key Concepts

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

X-Linked Inheritance

X-linked inheritance refers to the pattern of genetic transmission of traits or diseases that are associated with genes located on the X chromosome. In this case, males (XY) are more likely to express X-linked recessive diseases because they have only one X chromosome. If that X chromosome carries a defective gene, they will exhibit the disease, while females (XX) can be carriers if they have one defective X and one normal X.

Probability in Genetics

Probability in genetics involves calculating the likelihood of inheriting specific traits based on the genetic makeup of the parents. In this scenario, the probability of a son inheriting the disease can be determined by analyzing the combinations of chromosomes contributed by each parent. The father's defective X chromosome and the mother's normal X chromosomes create a specific set of possible outcomes for their offspring.

Punnett Square

A Punnett square is a diagram used to predict the genetic outcomes of a cross between two parents. It helps visualize the possible combinations of alleles that offspring may inherit. In this case, a Punnett square can be used to illustrate the potential genetic combinations of the father with the defective X chromosome and the mother with two normal X chromosomes, allowing for a clear calculation of the probability of the son inheriting the disease.

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a. How many different ways can the five officers be appointed?

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