With n multiple tests you are much more likely to approach the mean of positive results, which for an actually positive patient is (1-p1)n and for an actually negative patient is p2n, where p1 and p2 are false result probabilities. If p1, p2 << 1 then the means are sufficiently apart that you can compute the probability of getting your result (whatever that is) under the actual positive/negative scenario and one probability will be significantly higher than the other.