If a white woman and a black man have a child And another same couple has a child who has a child with the first child. What race will the new child be?

Answer 1

Wikipedia and many other sites sums up the question of race and racial identification quite neatly. They state:

"Some argue that although race is a valid taxonomic concept in other species, it cannot be applied to humans. Many scientists have argued that race definitions are imprecise, arbitrary, derived from custom, have many exceptions, have many gradations, and that the numbers of races delineated vary according to the culture making the racial distinctions; thus they reject the notion that any definition of race pertaining to humans can have taxonomic rigour and validity. Today most scientists study human genotypic and phenotypic variation using concepts such as "population" and "clinal gradation". Many contend that while racial categorizations may be marked by phenotypic or genotypic traits, the idea of race itself, and actual divisions of persons into races or racial groups, are social constructs. "

In this context, the question cannot be answered as the criteria for "white" or "black" cannot be determined without referring to the cultures definition of race. As an example in the "Old South" of the USA anyone with a negro ancestor would be considered a negro, although names for various gradations of "blackness" were in use. In South Africa during the apartheid period similar naming strictures applied. During the Spanish settlement of Central and South America specific names were developed for almost every combination of aboriginal, negro and European heritage.