Coefficient of inbreeding: A measure of how close two people are genetically to each another. The coefficient of inbreeding, symbolized by the letter F, is the probability that a person with two identical genes received both genes from one ancestor.
Take a first-cousin mating. First cousins share a set of grandparents. For any particular gene in the male, the chance that his female first cousin inherited the same gene from the same source is 1/8. Further, for any gene the man passes to his child, the chance is 1/8 that the woman has the same gene and ½ that she transmits that gene to the child so 1/8 X ½ = 1/16. Thus, a first-cousin marriage has a coefficient of inbreeding F =1/16.
The added risks for the offspring of first cousins depend not only upon the coefficient of inbreeding but also upon the genetic family history and test results. For example, first cousins of Italian descent are at increased risk of carrying a gene for beta thalassemia and genetic laboratory tests may confirm that they are both beta-thalassemia gene carriers.
There are always added risks in the mating of closely related persons and those risks are not entirely negligible.