An individual with an XXY genotype would possess 1 Barr body.
To explain further, Barr bodies are inactivated X chromosomes that are not expressing their genes in females (who typically have two X chromosomes). In males, normally with one X and one Y chromosome, there are no Barr bodies. However, in individuals with an XXY genotype, which is characteristic of Klinefelter syndrome, there is an additional X chromosome.
In this case, the formula to calculate Barr bodies is: number of X chromosomes – 1. Since an XXY individual has two X chromosomes, we subtract 1 from 2, resulting in 1 Barr body. Thus, the correct answer is 1.