To illustrate an intuitive and statistically valid method for combining independent sources of evidence that yields a p-value for the complete evidence, and to apply it to the problem of detecting simultaneous matches to multiple patterns in sequence homology searches. In sequence analysis, two or more (approximately) independent measures of the membership of a sequence (or sequence region) in some class are often available. We would like to estimate the likelihood of the sequence being a member of the class in view of all the available evidence. An example is estimating the significance of the observed match of a macromolecular sequence (DNA or protein) to a set of patterns (motifs) that characterize a biological sequence family. An intuitive way to do this is to express each piece of evidence as a p-value, and then use the product of these p-values as the measure of membership in the family. We derive a formula and algorithm (QFAST) for calculating the statistical distribution of the product of n independent p-values. We demonstrate that sorting sequences by this p-value effectively combines the information present in multiple motifs, leading to highly accurate and sensitive sequence homology searches.