The ability to perform whole-exome and, increasingly, whole-genome sequencing on large numbers of individuals has led to increased efforts to identify rare genetic variants that affect the risk of both common and rare diseases. In such applications, it is important to identify families that are segregating the rare variants of interest. For rare diseases or rare familial forms of common diseases, pedigrees with multiple affected members are clearly harbouring risk variants. For more common diseases, however, it may be unclear whether a family with a few affected members is segregating a familial disease, is the result of multiple sporadic cases, or is a mixture of familial cases and phenocopies. We provide calculations for the probability that a family is harbouring familial disease, presented in general terms that admit working guidelines for selecting families for current sequencing studies. Using examples motivated by our own studies of thyroid cancer and published studies of colorectal cancer, we show that for common diseases, families with exactly two affected first-degree relatives have only a moderate probability of segregating familial disease, but this probability is higher for families with three or more affected relatives, and those families should therefore be prioritised in sequencing studies.