The DNA profiles of two unrelated individuals can match (complete simi
larity) by chance alone. When the two individuals are related, the pro
bability of a coincidental match is higher. Here, I deal with the prob
abilities of coincidental matches for both related and unrelated indiv
iduals. The derivation starts from first principles; no prior knowledg
e is required. The results obtained by the method developed here are c
ompared with some other methods.