Say x is the percentage of an allele in your mom (or cousin, or brother). Say c is the filial similarity (brother=.5, son=.5, cousins=.125, etc.) of the allele. Say y is the general probability of having that allele in that population (assuming mom is the same species with you). Say f(x,y) is the expected value of the number of allele that you have.
Then f(x,y)= c * x+ (1-c) *y
In other word. There is no contradiction in the idea that we are 98% similar with monkeys and yet only 50% similar with our own mom.
Here, the world similar is used in totally different sense.
f(x,y) is 99% for most allele. Now let gy(x)=f(x,y) then
gy'(x) is c.
In other word, for every allele your mom have, it'll improve the expected value of you having the same allele by half. For each allele your cousin has, it'll improve the expected value of you having the same allele by 1/8th. That is for the same y. For most y, similarity is 100% nevertheless.
Say Ann, Beth, and Cindy has AA, Aa, and aa alleles.
Then Ann's sons have 25% higher expected value of having A alleles than Beth, and Beth have 25% higher expected value of having A alleles than Cindy. I say nothing of actual probability distribution.
Ann's cousins have .0625% higher expected value of A occurrence than Beth's cousins and .125% expected value of A occurrence than Cindy's cousins
Disclaimer: We do not take into account that people mate with those who are genetically similar but not too similar (i.e. no inbreeding).
Another way to see this is to look at y. For rare genes y is small. Hence.
50-50 is for genes that are rare and family specific. If your mother is color blind (100% carrier), the expected value of the number of color blind carrier is improved by 50%. It doesn't mean you'll be color blind. We'll have to go to the technicality of dominant vs recessive. But that's the idea.
For genes that are NOT rare, say genes that make you have 2 feet and 2 hand, you still share all your mom's genes. That's because everybody have that. Your mom have that, and your dad have that, and so is everyone else, including chimps.
Is this what most directly answer your question?
Again the issue is rarity. For rare genes P(You have it|mom have it) is 50%.
For common genes,
P(You have it|mom have it) = P(You have it and mom have it)/P(mom have it). //By bayesian rule
That is 1/1, which is true.
It's just obvious, probability = 1, that everybody has it.
Source: selfish gene by Richard Dawkins
I am a mathematician. Now prove me wrong.