Do siblings share 50% of their genes? (This is my first question on Maths Stack Exchange, I'm not sure if this is a maths question or a physics question ... or something else.)
I was watching this video about psychology, and it it the presenter asserts (at about 5:45) that:

Identical twins share ... 100% of their genes ... whereas non-identical twins, ... just like any brother and sister, share only 50% of their genes.

Now this doesn't seem quite right to me. I can accept that:


*

*Identical twins share 100% of each other's genes (being split from the same egg).

*Brothers and sisters (twins or not) share 50% of their parents' genes

Am I wrong in thinking that brothers and sisters don't necessarily share 50% of each other's genes?
 A: Assuming the parents share no common alleles , then each twin will inherit $50\%$ of each parent's set.  So for every gene, there is $50\%$ probability of both twins inheriting the same allele from a parent. There for the expectation is that the twins share half of their alleles.
However, since it is likely that the parents actually do share some (indeed, rather many) alleles, the expectation should be somewhat higher than one half.
A: First, think back to school biology and recall how inheritance works:


*

*Each parent has two versions of each gene.

*These two versions may or may not be identical.

*You inherit one from each parent, but it's random which you get.


So considering the copies as distinct, the two siblings will inherit about $50$% of the same copies of their mother's genes, and about $50$% of the same copies of their father's genes.
So in that sense, they'll have about $50$% of their genes in common.
Now, what if one of your parents has two identical copies of a gene? Does it make sense to distinguish between the two? Not really. So there's now $100$% probability (neglecting mutations) that both siblings inherit the same version of the gene from that parent.
And if the gene happens to be one where a difference in one copy would be fatal, each parent is guaranteed to have only the non-fatal version, as are the two children.
But in any case, the likelihood of a parent having two matching copies depends on how common each version is in the general population.
Finally there's the question of what constitute identical genes. Are they ones with identical base pairs throughout? Or merely ones whose resulting function is essentially the same? How different is their DNA allowed to be?
In fact, we have most of our DNA in common with all human beings, and a lot in common with all multicellular organisms. I'm unsure of the figures, but this is likely to mean that in that sense, the common DNA between the two siblings is far closer to $100$% than to $50$%.
So the answer is that, treating each parent's two copies as distinguishable, the two siblings inherit about $50$% of the same genes—but that a lot of the time, the inherired "different" genes won't actually be distinguishable.
A: Now, the specific mathematics - humans have $23$ chromosome pairs. If nothing goes funny (not at all a safe assumption), a person gets one chromosome from each parent in each pair, chosen at random. For simplicity, we will count on the chromosome level, and assume that none of the parents' chromosomes are the same as each other.
In each pair, then, a pair of full siblings get the same chromosome from their mother half the time and the same chromosome from their father half the time. $46$ chromosomes, an average of $23$ shared. But that's only an average; each chromosome is independent here, and random variation happens. That's a standard deviation of $\sqrt{11.5}\approx 3.6$, fairly large compared to the mean. About $1.3\%$ of the time, two full siblings will share $15$ or fewer chromosomes, less than a third of the same genes.
[Edit] Recombination changes these numbers, significantly decreasing the variance in how much genetic material matches. I don't have enough data to put solid numbers on that.
For more distant relations, the matching genes drop by half for each degree of separation (either a parent, a child, or a full sibling relation) - grandparents or aunts/uncles are an average of $\frac14$, first cousins are an average of $\frac18$, and so on. At six degrees, it's an average of less than one matching chromosome - which is about the point that incest stops being a taboo anyone cares about.
