Heidi R. answered 07/02/19
Focused, Fun and Effective!
I can speak to part of your inquiry without pulling out my reference books.
"Provided that a man with blue eyes and a woman with brown eyes have a child, can the probability of their child to have blue eyes be calculated?"
Yes, it can be calculated. However, first it would need to be determined if the woman is a carrier for the non-dominant gene. Typically one would want to go back at least 2 additional generations to exclude or include probabilities for grandparents and great-grandparents having brown eyes but carrying the recessive gene.
For example, two persons could have children and both have brown eyes. Both could carry the recessive and increase the likelihood of passing on the "invisible" trait. On the other hand, only one parent may have brown eyes and carry the recessive, thus reducing the possibility of occurrence.
Good luck on identifying all of the variants!
--Heidi