Question

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

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

Step-by-step solution

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.

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: \(\dfrac{1}{2}\).

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 \(\dfrac{1}{1024}.\)