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 Jun 29 revised calculating 2 sums of series Fixed plural of "series" Jun 29 comment calculating 2 sums of series FYI, the plural of "series" is "series". Jun 29 suggested approved edit on calculating 2 sums of series Jun 6 awarded Yearling May 6 awarded Caucus Nov 29 comment Conditional probability of cows @Sarastro I just realized we are interpreting the question much differently. I interpreted it as "If you see only two cows and they are both black...". I think you have interpreted it as: "If you see all the cows and exactly two of them are black...". I think either interpretation could be correct based on the original post. However, I have produced the expected answer of 0.3, so my interpretation may have been the intent of the question's author. Nov 29 awarded Commentator Nov 29 comment Conditional probability of cows @Sarastro No it isn't. The question assumes we are looking at the black side; the other side(s) are irrelevant. The question says "if you see two black cows", so if you see the multi-sided cow, it has to be on the black side; otherwise, you wouldn't be seeing two black cows. Nov 29 comment Difference between $\sum$ and $\int$ In your summation picture, the center of each rectangle should be on the line. This would demonstrate how the summation end up being a higher value than the integration. Nov 29 comment Difference between $\sum$ and $\int$ It's because integration gives an exact calculation of area under the curve, which in this case turns out to be a little less than the very crude estimation you get by doing a summation. The summation is like a Riemann sum with big rectangles instead of infinitely small ones. Nov 29 answered Difference between $\sum$ and $\int$ Nov 29 comment Conditional probability of cows @Sarastro If the cow had 1000 sides, my answer would be the same. If I saw two black sides, there would still be the three possibilities I list above, and the probability would be 0.66. Remember, you start with the assumption that you see two black sides, so you do not need to calculate the probability that the n-sided cow is showing it's black side. Nov 28 revised Rolling die until number is greater than 100 added 371 characters in body Nov 28 comment Rolling die until number is greater than 100 @Jean-Sébastien They don't have to be equally likely. There are still $a_{98}$ + $a_{97}$ + $a_{96}$ + $a_{95}$ + $a_{94}$ more ways to get 100 than there are to get 105. Nov 28 answered Rolling die until number is greater than 100 Nov 28 comment Conditional probability of cows I think @Johan is right. I updated my answer accordingly. Nov 28 revised Conditional probability of cows added 614 characters in body Nov 28 comment Conditional probability of cows If you give the condition "if you see two black cows", then you assume exactly that. The probability of seeing a white cow is zero if you start with the condition "if you see two black cows". Nov 28 comment Conditional probability of cows Your question reads "if you see two black cows". Did you mean "if you see two cows"? Nov 28 answered Conditional probability of cows