Despite the many successes of cancer research, we lack the framework necessary to predict the ratio of familial (inherited) to sporadic (non–inherited) cancers. An evolutionary model of multistage carcinogenesis provides this framework by demonstrating that the number of tumour suppressor loci (TSLs) preventing cancer in a given tissue is expected to depend upon the tissue's vulnerability to pre–reproductive somatic mutation. Since this vulnerability increases with tissue size, single gene control of human cancer may be restricted to retinoblastoma, a cancer of the tiny embryonic retina. The model is used to estimate the frequency of mutant alleles causing inherited cancers, based on the population genetics of the mutation–selection balance between new mutations arising and selection that eliminates them. For each specific cancer, this balance is determined by the effectiveness with which pre–reproductive cancer is suppressed in the non–mutant genotype characteristic of that population. Effectiveness depends on an interaction between the number of TSLs suppressing the cancer and factors determining the tissue–wide somatic mutation rate, such as tissue size and number of pre–reproductive cell divisions. The model predicts that the commonest pre–reproductive cancers will have the lowest proportion of familial cases, and that cancers associated with the most TSLs will have the highest post–reproductive incidence but no elevated pre–reproductive risk (a pattern seen in human epithelial cancers).