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: \(\frac{1}{1024}\)

Step-by-step solution

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.

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 \(\frac{1}{2}\).

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: \( \text{Probability} = \frac{1}{2} \times \frac{1}{2} \times ... \times \frac{1}{2} = \left(\frac{1}{2}\right)^{10}\)

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