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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: The probability is \(\dfrac{1}{1024}\).

Step by step solution

01

Understanding Independent Assortment

In sexually reproducing organisms, the chromosomes in a gamete are a random mix of maternal and paternal chromosomes due to the independent assortment of homologous chromosomes during meiosis. Since there are haploid number (n) of chromosome pairs, there will be \(2^n\) possible combinations of maternal and paternal chromosomes in the gametes produced.
02

Calculate the probability for one chromosome

As there are two homologs for each chromosome, one maternal and one paternal, we have a 50% chance (1 in 2) of selecting the maternal homolog for each chromosome in the sperm cell. This can be expressed as a probability: \(\dfrac{1}{2}\).
03

Calculate the probability for all chromosomes

Since each chromosome is independently assorted, we multiply the individual probabilities to get the probability of all 10 chromosomes having maternal centromeres in the sperm. The probability of all 10 chromosomes having maternal centromeres = \(\left(\dfrac{1}{2}\right)^{10} = \dfrac{1}{1024}\). So, the probability that a sperm will be formed with all 10 chromosomes having maternal centromeres is \(\dfrac{1}{1024}.\)

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Most popular questions from this chapter

Cell division cycle mutations render the mutants unable to continue the cell cycle. This phenotype creates a paradox where mutant cells must also be grown in the lab to further identify the gene and study the role of the protein. How do you think this problem can be solved?

Contrast the genetic content and the origin of sister versus nonsister chromatids during their earliest appearance in prophase I of meiosis. How might the genetic content of these change by the time tetrads have aligned at the equatorial plate during metaphase I?

During the first meiotic prophase, (a) when does crossing over occur; (b) when does synapsis occur; (c) during which stage are the chromosomes least condensed; and (d) when are chiasmata first visible?

Compare chromosomal separation in plant and animal cells.

A species of cereal rye (Secale cereale) has a chromosome number of \(14,\) while a species of Canadian wild rye (Elymus canadensis) has a chromosome number of \(28 .\) Sterile hybrids can be produced by crossing Secale with Elymus. (a) What would be the expected chromosome number in the somatic cells of the hybrids? (b) Given that none of the chromosomes pair at meiosis I in the sterile hybrid (Hang and Franckowlak, 1984 ), speculate on the anaphase I separation patterns of these chromosomes.
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