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I've been learning all these laws about Sekefot-doubts, but I'm coming up shy on a basic point. What is considered a Safek? Example:if there are 100 pieces of lettuce and I check all of them and only find one bug on one piece of lettuce, this means that 1/100 are the chances that I'll find another in my next batch of 99%. Is 1/100 a Safek Deroayta or is it just such a small chance that we say the Rov is too overpowering to Oser?

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If anyone understands what I'm trying to ask please edit for others to better understand. –  Hacham Gabriel Sep 10 '13 at 13:30

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Contemporary poskim discuss how to approach statistics -- we tend to work with concepts of mi'ut hamatzui -- a "commonly occurring though less than 50% event", for which we do need to check; vs. mi'ut sh'eino matzui -- a rare event, for which we don't.

Many poskim treat 10% as the cutoff line for mi'ut sh'eino matzui, based on a fascinating application from the laws of Trumah, about when we need to check if wine has spoiled, to laws of sales, regarding the normal spoilage rates of wine in Talmudic times.

Furthermore we have the distinction of ruba d'ita kaman, i.e. we know there is a bug someplace in this bag, vs. ruba d'leita kaman, we know in a theoretical sense that occasionally there are bugs.

Rabbi JD Bleich addresses this in a Tradition article c. 2007: let's assume that 5% of dairy cows are treifot. That means that 5% of cows produce non-kosher milk. Now if I buy a bottle of milk made at a commercial dairy, it was mixed together from many different cows, meaning that on average 5% of this bottle is non-kosher -- and 5% is not batel! Answer: we apply ruba deleita kaman -- the statistic of 5% is an abstract one. Therefore, take any given cow, and we rule: "we assume this cow is kosher. 100%." Take the milk from that cow, and it's kosher. 100%.

Specifically with regards to miut, safek, hazaka and the like as applied to bugs in food, see Rabbi Eitam Henkin's book Lakhem Yihyeh Le-Okhlah.

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Related question: judaism.stackexchange.com/q/27862 –  Fred Sep 10 '13 at 17:00
    
Based on judaism.stackexchange.com/a/57314/9275, perhaps we should interpret the statistical answer in a belief-based sense. In other words, we don't conduct many tests on many lettuces, but instead to establish a 10% safek shiur, we ask, "If I received 1 dollar if there were no bug, but paid 10 dollars if there were a bug, would I consider that a good deal?" In particular, the shiur might be evaluated differently by different people in different situations in a ruba d'leita kaman situation. –  Daniel Moskovich 2 days ago
    
@DanielMoskovich fascinating but I don't think so. If the average human being doesn't KNOW with normal senses that A will cause B, then if he does A on Shabbos and B occurs, that's not called "thoughtful labor" (mileches machsheves). Using my normal human senses, I can't tell whether this bench will dig a hole. Contrast to checking my wine for spoilage or lettuce for bugs -- it's something I certainly could do, but the halacha says I'm not obligated to do so if the probability is sufficiently low. And the Talmudic precedent for that seems to be an objective one. –  Shalom 2 days ago

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