Final answer:
Dan's mother produced an egg carrying the u allele through the process of meiosis and genetic recombination.
Step-by-step explanation:
The production of an egg carrying the u allele by Dan's mother can be explained through the process of meiosis and genetic recombination. Each parent contributes one set of chromosomes to the offspring, including one copy of each allele. During meiosis, the genetic material from the parent cells is shuffled and recombined, resulting in new combinations of alleles in the egg. This allows for the possibility of the egg carrying the u allele, despite the usual production of one egg per month.