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Jun
6
awarded  Yearling
May
6
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Dec
12
revised Probability of drawing three letters out of four
deleted 3 characters in body
Dec
12
answered Probability of drawing three letters out of four
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
Nov
27
awarded  Nice Answer