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"\n",
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"# A Concrete Introduction to Probability (using Python)\n",
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"\n",
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"In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n",
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"In 1814, Pierre-Simon Laplace provided a classic [definition](https://en.wikipedia.org/wiki/Classical_definition_of_probability) of probability:\n",
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"\n",
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">*Probability theory is nothing but common sense reduced to calculation. ... [Probability] is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n",
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"\n",
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"||\n",
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"| |\n",
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"|--|\n",
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"||\n",
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"|<a href=\"https://en.wikipedia.org/wiki/Pierre-Simon_Laplace\">Pierre-Simon Laplace</a> (1749–1827)|\n",
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"\n",
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"Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/search?q=probability+ball+urn). (You'd think the urns would be empty by now.)\n",
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"\n",
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"||\n",
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"| |\n",
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"|---|\n",
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"||\n",
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"|<a href=\"https://en.wikipedia.org/wiki/Jacob_Bernoulli\">Jacob Bernoulli</a> (1655–1705)|\n",
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"\n",
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"But in a sense it is curious that we were able to solve this problem with the same methodology as the others: this problem comes from a section of Downey's book titled **My favorite Bayes's Theorem Problems**, so one would expect that we'd need to invoke Bayes Theorem to solve it. The computation above shows that that is not necessary.\n",
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"\n",
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"||\n",
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"| |\n",
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"|---|\n",
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"||\n",
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"|<a href=\"https://en.wikipedia.org/wiki/Thomas_Bayes\">Rev. Thomas Bayes</a> (1701-1761)|\n",
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"\n",
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"All you ever needed to know about probability problems you learned from Sesame Street:\n",
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"\n",
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"||\n",
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"| |\n",
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"|---|\n",
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"||\n",
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"|<a href=\"https://en.wikipedia.org/wiki/Count_von_Count\">The Count</a> (1972—)|\n",
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