As a species, humans actually show remarkably little genetic diversity. The DNA of two unrelated people only differs by about one in every 1,000 base pairs; orangutans differ by more than double this amount. Even so, there are three billion base pairs in the human genome, so that’s an average of three million genetic differences between any two strangers.
Most of these differences are ‘single nucleotide polymorphisms’ (SNPs), in which a single letter of the genetic code is changed. There are about 20 million known SNPs in the human genome. This means that the odds l of someone having the same DNA by chance is like having a deck of 20 million cards, all different, and then drawing the same hand of three million cards twice!