Rabbi Yohanan teaches that there are three cases where, in situations of doubt, the Sages ruled that we will assume that a given case will be like the majority of similar cases where there is no doubt. The three cases – the ‘source’, the ‘placenta’ and the ‘piece’ – all deal with cases of ritual cleanliness and defilement. The Gemara points out that in other areas of Jewish law we find many cases where the Sages rule that we follow the rov – the majority.
Perhaps the most famous case of following rov appears in the Gemara in a number of places. When there are nine shops all of which were selling shehutah – ritually killed meat – and one shop that was selling nevelah – non-kosher meat – and a man entered one of the stores and purchased some meat, but he does not know in which of them he bought it, the meat is forbidden on account of the doubt. If, however, he found the meat outside of the stores, we follow the rov – the rule of the majority – and assume that the meat that he found is kosher meat.
The fact that if the meat was purchased in the store it is forbidden, but if it was found outside of the store it is permitted, demands justification.
The idea that we assume that a given thing came from the majority makes sense intuitively and is codified in the Talmud as kol de-parish, me-ruba parish – anything that is separated is assumed to have come out of the majority. This stands in contrast with something that remains in its original place, about which the Talmud rules mehtza kol kavu’a ke-mehtza al dami – that any doubtful thing that has not moved from its place is viewed as being balanced, 50:50. For this reason, the rule of rov cannot be applied.
One explanation for this is that so long as something is in its original place, we cannot view it as becoming batel – nullified – by the majority, and we need to acknowledge the possibility that the object came from that place.
In recent years, mathematicians have worked on explaining these rules based on the laws of probability. See Dr. Moshe Koppel’s “Resolving Uncertainty: A Unified Overview of Rabbinic Methods” at http://u.cs.biu.ac.il/~koppel/rov-traditionversion.pdf