Say my mom has a gene (it's one of those regular gene, ignore X and Y chromosome)
The gene exist in p% of the population.
Things get complicated due to that p. If p is 100%, for example, then of course the probability that I have the gene to is 100%. If p is 1% then the probability that I got the gene will be 50%.
How to formalize this mathematically?
My gut feeling is it'll just be linear. if p is 1% then my chance will be 50.5% because that means my dad have a 1% chance to have that gamete.
Then i want to extend this to cousins.