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by turaw 3740 days ago
Did anyone else learn how to compute probabilities by drilling through the algebra? Like, if asked how to convert a plain English probabilistic query (e.g. "what is the chance of picking two red candies from a mixed bowl") into a formula, I would focus on the 'and', mentally recite something to the effect of 'conjunctions multiply probabilities', then write p(red)*p(red). There's no intuition or understanding, just rote memorization.

I've been trying to recognize and account for this deficiency by drawing mental decision trees enumerating probabilities instead ... anyone else doing anything similar?
2 comments
grayclhn 3740 days ago
Not to be an asshole but, unless you replace the first candy after taking it out, your formula's wrong.

If you start w/ 50 red candies and 50 non-red candies, the chance of the first one red is 1/2 (from 50/100) but the chance the second one is red after first drawing a red candy is now 49/99. After removing one red candy, there are now 49 red candies and 99 total candies.

So, P(red) * P(red | removed 1 red) = 49/198

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turaw 3736 days ago
XD okay, fair enough. I was thinking of the ideal candy bowl, which is self-refilling. Do you grade undergraduate stats quizzes, by the way?
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todd8 3740 days ago
Drake's Fundamentals of Applied Probability Theory does emphasize the tree enumeration of possibilities in it's presentation of probability. It's an excellent introductory text. I remember remarking to a fellow student that the book was so good you didn't need to go to lecture. His reply was that Professor Drake's lectures were so good you didn't need to read the book.

However, in probability thing can quickly get complicated and, for me at least, intuition can't always be trusted. (I probably needed to go to the lectures and read the book.) For examples see either Schwarz's 40 Puzzles and Problems in Probability and Mathematical Statistics or Grimmett and Stirzaker's larger One Thousand Exercises in Probability.

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turaw 3736 days ago
Aah, that's excellent, thank you very much! I'm always on the lookout for interesting course ware and that's quite the strong recommendation.

And those look like excellent exercises as well; thank you doubly :)

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