HLA genes are a type of proteins that are responsible for cell recognition, that is, they allow cells from the immune system to differentiate between own tissues and external substances.
The HLA system of each person consists of a set of genes that are inherited in groups, which are called haplotypes. Humans inherit one haplotype from the father and the other from the mother. For this reason, there are four possible combinations of haplotypes in the children of each couple, as we can see in this picture.
For siblings to be histocompatible, they must have exactly the same haplotypes. The chances for this to happen are 25%.