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Chapter 2: Problem 18

What is the probability that, in an organism with a haploid number of \(10,\) a sperm will be formed that contains all 10 chromosomes whose centromeres were derived from maternal homologs?

Short Answer

Expert verified
Answer: \(\frac{1}{1024}\)

Step by step solution

01

Understanding Independent Events

Independent events are those events that do not affect the occurrence of one another. In this case, the inheritance of each chromosome with a centromere from maternal homologs is independent of the others.
02

Calculating the Probability for a Single Chromosome

For a single chromosome, there are two possibilities: it can either have a centromere from the maternal homolog or from the paternal homolog. Since these possibilities are equally likely, the probability of having a centromere from the maternal homolog for a single chromosome is \(\frac{1}{2}\).
03

Using the Multiplication Rule for Independent Events

Since we have 10 chromosomes and the events are independent, the probability of all chromosomes having centromeres from maternal homologs is simply the multiplication of the probabilities for each chromosome: \( \text{Probability} = \frac{1}{2} \times \frac{1}{2} \times ... \times \frac{1}{2} = \left(\frac{1}{2}\right)^{10}\)
04

Calculate the Final Probability

Now we can calculate the probability: \( \text{Probability} = \left(\frac{1}{2}\right)^{10} = \frac{1}{1024}\) So the probability that a sperm will be formed containing all 10 chromosomes whose centromeres were derived from maternal homologs is \(\frac{1}{1024}\).

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Most popular questions from this chapter

In this chapter, we focused on how chromosomes are distributed during cell division, both in dividing somatic cells (mitosis) and in gamete- and spore- forming cells (meiosis). We found many opportunities to consider the methods and reasoning by which much of this information was acquired. From the explanations given in the chapter, answer the following questions. (a) How do we know that chromosomes exist in homologous pairs? (b) How do we know that DNA replication occurs during interphase, not early in mitosis? (c) How do we know that mitotic chromosomes are derived from chromatin?

During oogenesis in an animal species with a haploid number of \(6,\) one dyad undergoes nondisjunction during meiosis II. Following the second meiotic division, this dyad ends up intact in the ovum. How many chromosomes are present in (a) the mature ovum and (b) the second polar body? (c) Following fertilization by a normal sperm, what chromosome condition is created?

Explain why meiosis leads to significant genetic variation while mitosis does not.

Discuss the concepts of homologous chromosomes, diploidy, and haploidy. What characteristics do two homologous chromosomes share?

What role do the following cellular components play in the storage, expression, or transmission of genetic information: chromatin, (b) nucleolus, (c) ribosome, (d) mitochondrion, centriole, (f) centromere?
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