The Ksav V’Kabbalah at the end of parshas Bechukosai brings up a sugya which deserves mention due to the enormous amount of ink spilled by Achronim discussing it, but I’m afraid all I’m going to give for now is roshei perakim due to lack of time and my lack of research into it (but feel free to comment away!) The scenario: after a customer purchased a side of beef at the local butcher, it was discovered that one of the cows put up for sale was a treifa. Using the rule of thumb of kol d’parish m’ruba parish, the customer assumes that his side of beef is part of the rov and is kosher. Yet we also have a rule of kol kavua k’machtza al machtza. If anyone were to now walk into the store to purchase a side of beef, the rule of kavua tells us that every hide of beef has an only 50/50 chance of being kosher, and hence may not be eaten (safeik d’oraysa l’chumra). But how can this be? If the side of beef the customer took home is kosher, how every side of beef remaining in the butcher store, including potentially the side of beef from the same cow bought by the customer, be treif?!
The Kv"K cites the K'reysi, who suggests an answer based on a din in hilchos ma’aser beheima (end of Behukosai). If an animal counted for ma’aser beheima jumps back into the herd, the halacha (Bava Metziya 6) is that the entire herd is patur from ma’aser. The reason why is because every tenth animal counted is potentially the one which jumped back in and an animal already counted is patur. The Rishonim (quoted in Shita Mekubetzes) ask: but isn't this one animal bateil in the entire herd? They answer that the Torah demands asiri vaday – the definitive 10th animal – for ma’aser beheima. Rov tilts the odds in favor of any animal being counted not being the one that jumped back in, but a high degree of certainty – good odds – is not the same as definitive truth. In lomdishe terms, rov is mevarer the safeik, not machriya the safeik. (Side note: note that the question here dealt with bitul b'rov, but the answer speaks to the rule of kol d'parish... how are these concepts related is a long discussion in its own right!)
Returning to our butcher store case, if we declared with certainty that the meat in the customer’s possession is from a kosher cow, we would indeed be hard pressed to justify declaring a side of beef from the same cow treif! But that’s not how rov works. In reality we don’t know whether the side of beef in the customer’s possession is kosher – all we have is a probability of rov. There still remains a doubt whether the meat is really kosher or treif, and there remains a doubt as well whether the corresponding side of beef in the butcher store is kosher or treif. Kok d’parish and kol kavua do not determine physical reality – they just provide two different ways of relating to uncertainty. Sometimes meat can be eaten despite the doubt that it may be trief, sometimes not.
The Ksav v’Kabbalah is not happy with this approach based on a question from Kesubos 15 that we once discussed (here). He follows up with an answer he received from from R’ Akiva Eiger, but this post is long enough for now, so if you want more you'll have to read it inside (link).