Gemara

(Beraisa): If nine stores sell Kosher meat and one sells Neveilah, and one bought from a store and he is unsure from which, the meat is forbidden. If meat is found, we follow the majority.

Pesachim 9b: If there were nine piles of Matzah and one of Chametz, and a mouse took a piece from a pile, and we do not know from which it took, this is like the case of nine stores (the Reisha).

If a piece separated from a pile and a mouse took it, this is like the Seifa.

Kesuvos 15a (R. Zeira): Any Safek about an Isur Kavu'a (it is from a place where the Isur is known) is always considered an even Safek, whether this is a leniency or a stringency.

D'Vei R. Yanai taught that Chachamim expound "he waits in hiding" to exempt one who throws a rock into a crowd (and killed someone).

Suggestion: At most half of the crowd are Yisraelim.

Rejection: We are always lenient about a Safek in capital cases! (We would not need a verse to teach the law.)

Rather, there are nine Yisraelim and one Nochri. Since they are Kevu'im, it is considered an even Safek.

Rishonim

Rif, Rosh and Rambam (Chulin 33b, 8:20 and Hilchos Ma'achalos Asuros 8:11): If nine stores sell slaughtered meat and one sells Neveilah, and one bought from one of the stores and does not know from which, the meat is forbidden.

Rif and Rosh: If it was found in a Nochri's hand, it is permitted.

Ran (DH uv'Nimtza): When something is found, we assume that it separated from the majority, i.e. if we did not see it separate. If we saw it separate from Kavu'a, even though it came to us only afterwards, it is like Kavu'a. A proof is from Pesachim 9b. If a mouse took a piece from a pile, and we do not know whether it took from a pile of Matzah or of Chametz, this is like the case of nine stores. Even though the mouse brought it into the house only after it separated, since we saw it separate, it is like an Isur Kavu'a. I say that if it did not come to us from a place of Kevi'us, even though we saw it separate from there, letter of the law it is permitted. Mid'Oraisa, Kavu'a is only when he takes from a place of Kevi'us. Chachamim decreed when one saw it separate, lest one take from Kavu'a.

Rambam: Every Isur Kavu'a is like an even Safek. If meat is found in the market, we follow the majority. Anything that separated is assumed to be from the majority.

Magid Mishneh: The Rashba forbids an Isur Kavu'a by itself. If it became mixed with a majority of Heter and it is not recognized, it is permitted, for it is a Sefek-Sefeka (two doubts). He permits even a piece that is Re'uyah Lehiskaved (important enough to be served to honor a guest).

Teshuvas ha'Rosh (20:17): When a piece separated from the mixture in front of us, the Safek started in a place of Kevi'us. We have no source to decree when a piece separated before there was a Safek, e.g. one bought meat and later we heard that there was a Tereifah in the market.

Poskim

Shulchan Aruch (YD 110:4): If most stores sell slaughtered meat and the minority sell Neveilah, and someone bought from a store and does not know from which, if the meat became mixed with other meat and it is not recognized, it is Batel is the majority, for it is a Sefek-Sefeka.

Beis Yosef (DH u'Mah she'Chasav Kegon): The Rashba says that when an Isur is Kavu'a in its place, e.g. one does not know whether he bought from a store that sells slaughtered or Neveilah meat, a piece is not Batel in the majority. This is even if it is not Re'uyah Lehiskaved. If the Isur was found in front of the stores, i.e. it was not taken from the place of Kevi'us, it is Batel even if it is Re'uyah Lehiskaved. The Tur teaches that an Isur not recognized in its place is Batel only if it is not important. It does not depend on whether or not it separated. When the Isur is recognized in its place, we say oppositely. It does not depend on whether or not it is important, rather, only on whether or not it separated. If it separated, even a Chatichah ha'Re'uyah Lehiskaved, which is very important, is permitted. If one took it from the mixture, it is forbidden.

Tur (citing the Rashba): Therefore, if meat is found in a Nochri's hand, even though it is known that they buy only from the markets, and we do not know from which he bought, it is permitted, for the Safek arose after it separated. However, if we saw him leave the store, the Safek arose then, in the place of Kevi'us, so it is forbidden. It seems to me that it is forbidden only when it is by itself, but if it became mixed and it is not recognized, it is Batel is the majority, for it is a Sefek-Sefeka.

Beis Yosef (DH v'Chasav): 'Therefore' in the Rashba does not refer to the above law, that if it separated in front of us it is as if it is still in its Kevi'us and it is forbidden. This is the same exact law! Rather, it refers to the primary law, that if one bought from the store it is forbidden, and if it was found in front of the stores we follow the majority.

Rebuttal (Bach 5 DH u'Mah): 'It seems to me' refers to the previous law, when it separated from Kavu'a in front of us. It is forbidden only by itself, but not if it became mixed. Even if it is a Chatichah ha'Re'uyah Lehiskaved, it is permitted due to Sefek-Sefeka. 'It seems to me' does not refer to one who bought from where it is truly Kavu'a. Then we cannot permit due to Sefek-Sefeka, since the first Safek is mid'Oraisa. The Rashba teaches that when it separated from Kavu'a, even though Chachamim forbid it as if it were Kavu'a, it is not totally like Kavu'a. It is forbidden only by itself. The Beis Yosef understood that 'it seems to me' refers even a case of actual Kavu'a, and so he wrote in the Shulchan Aruch. May Hash-m pardon his mistake!

Tur: The Rashba wrote that even if half the mixture fell elsewhere (we are lenient to assume that the Isur was not among them). This is only if the first mixture was permitted mid'Oraisa.

Bach (14): This is astounding. An Isur Kavu'a is (forbidden) mid'Oraisa, like we learn in Kesuvos 15a. If so, a Sefek-Sefeka should not permit this, since the first Safek is mid'Oraisa! Why does the Rashba permit due to Sefek-Sefeka? He permits only when one saw someone leave the market holding meat. This is Kavu'a only mid'Rabanan. Mid'Oraisa it is Kavu'a only if he took from the place of Kevi'us. If he saw it separate from there, it is Kavu'a only mid'Rabanan, like the Ran says. The Rashba permits due to Sefek-Sefeka only in such a case. He brought a proof from a ring of idolatry (mixed with permitted rings). If one separated in front of us, it is forbidden, but if the one that separated fell into Heter, it is permitted due to Sefek-Sefeka. However, Isur v'Heter says that whenever the Safek arose in a place of Kevi'us, even if it separated in front of us, we do not permit due to Sefek-Sefeka. That Heter is only if the Nochri found or bought it not in front of us. Then, the Rambam permits. It is proper to be stringent.

Shach (22): Also Isur v'Heter says that the Rashba permits only when it separated in front of us, for this is mid'Rabanan. The Rashba connotes like this in Toras ha'Bayis ha'Katzar. In Toras ha'Bayis ha'Aruch, he says 'this is only if it the piece he took from Kavu'a did not get mixed with others.' However, perhaps he refers to a Chatichah ha'Re'uyah Lehiskaved, which he was discussing there. He and the Poskim call such mixtures 'Kavu'a'. There also, the first Safek is mid'Rabanan, therefore if it is mixed with others it is permitted due to Sefek-Sefeka. However, the Magid Mishneh says that the Rashba permits what was taken from Kavu'a if it became mixed. He did not mention Chatichah ha'Re'uyah Lehiskaved. It is difficult to say that he discusses a Nochri who took, for he did not specify. Also, he already taught this above! If we could say that he discusses a Nochri, we could say the same for the Mechaber. The Levush says otherwise. Rather, the Rashba and Magid Mishneh discuss a Yisrael who bought from the stores. Toras ha'Bayis connotes that a Nochri who bought is like a Yisrael who bought, and it is forbidden mid'Oraisa. Also Isur v'Heter says so, and the Rema (Toras Chatas) in the name of Tosfos. The Rashba and Mechaber say that a Safek Terefah is not Batel in a majority. This is because Kavu'a is a Chidush, for usually we follow the majority. Therefore, we learn only the Chidush, i.e. when it is by itself, but not if it was mixed.

Question (R. Akiva Eiger): In Sa'if 8, if one of the mixture fell into others, we forbid because this is like Kavu'a (if it separated in front of us, according to the Rashba, or due to a decree lest one take from Kavu'a, according to the Rosh). Even Kavu'a mid'Rabanan forbids a second mixture. All the more so Kavu'a mid'Oraisa forbids a second mixture! This requires great investigation.

Gra (10): If a ring of idolatry became mixed, and one of the mixture became mixed, we permit. Regarding pomegranates of Badan we forbid, until there is a third mixture. Since they are important, Chachamim made the first mixture like Vadai Isur. We say similarly about living animals. The third mixture is permitted due to Sefek-Sefeka. The Rashba's text permits even the second mixture of pomegranates. This is better, for usually idolatry is more stringent than other Isurim. According to our text, we can say that we need three mixtures to permit eating them at once. If there were only two mixtures, it is a single Safek to eat all at once. The Ri forbids a Sefek-Sefeka when one Safek is about the item itself, and the other is due to a mixture. The Rashba explains that both Sefekos must be about the item, or both about the mixture. Many explain that since the Torah forbids a Safek, this is like a Vadai Isur that became mixed. We cannot permit due to Sefek-Sefeka, since if an Isur became mixed with only of Heter, we would forbid this mixture due to Safek. Tosfos (Chulin 95a DH Hachi) says that we decree when one of a mixture became mixed, lest he take from Kavu'a, but we do not decree when a known Isur became mixed. The Rashba forbids what separates in front of us is like Kavu'a. Something important is not Batel mid'Rabanan, but it is not like Kavu'a. R. Tam permits even when one Safek is about the item and the other is due to a mixture. The Rashba holds like R. Tam, but says that one should be concerned for the Ri. The Rambam requires three mixtures because the first is considered Vadai. Therefore, if the first is a Safek, two mixtures suffice. The Rema in Sa'if 8 rules like the Rambam.

Rema: Some forbid in this case. This is because whenever the Isur is (Kavu'a) in its place, it is like an even Safek. Since the Torah forbids the first Safek, and there is not another Safek to permit, only the mixture, this is not called a Sefek-Sefeka. The custom is like this.

Shach (26): The Rema gave a general rule (whenever...) to teach that even if it separated or the Nochri bought it in front of us, since the Isur was (Kavu'a) in its place, it is like an even Safek. However, in such a case, if it became mixed we can permit if needed to avoid a big loss. This is because the Maharshal rules like the Rashba, and the Ran and others say that when it separated in front of us, it is only mid'Rabanan. However, this does not permit eating them together, for then it is not a Sefek-Sefeka.

Gra (11): Here the Rema rules like the Ri.

Rema (8): If a Safek became mixed, and one of them became mixed with others, the latter mixture is permitted.