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?

Verified step by step guidance

1. Understand that the organism has a haploid number of 10, meaning each gamete (sperm) will contain 10 chromosomes, one from each homologous pair.
2. Recognize that for each homologous chromosome pair, there are two possible centromere origins: maternal or paternal.
3. Since the question asks for the probability that all 10 chromosomes in the sperm have centromeres derived from the maternal homologs, consider that each chromosome pair independently contributes either the maternal or paternal centromere with equal probability (assuming no bias).
4. Calculate the probability for one chromosome to have the maternal centromere, which is \(\frac{1}{2}\), and then raise this probability to the power of 10 (the number of chromosome pairs) to find the combined probability for all chromosomes.
5. Express the final probability as \(\left(\frac{1}{2}\right)^{10}\), representing the chance that all 10 chromosomes in the sperm carry maternal centromeres.

Key Concepts

Haploid Number and Chromosome Composition

The haploid number represents the number of chromosomes in a gamete, which is half the diploid number. In this case, the organism has 10 chromosomes in its haploid set, meaning each sperm normally contains one chromosome from each homologous pair, either maternal or paternal.

Independent Assortment of Chromosomes

During meiosis, homologous chromosomes segregate independently, so each chromosome in a gamete has a 50% chance of being maternal or paternal in origin. This random assortment leads to genetic variation in gametes.

Probability of Inheriting All Maternal Homologs

Since each chromosome has a 1/2 chance of being maternal, the probability that all 10 chromosomes in a sperm are maternal is (1/2)^10. This reflects the combined independent probabilities of inheriting each maternal chromosome.