Sets and Probability
stopa.io
Sets and Probability
1–10 of 38 posts
Re: Sets and Probability
#2This was so satisfying to read.
Re: Sets and Probability
#3This was so satisfying to read.
Thank you for the kind words :)
Re: Sets and Probability
#4The set-based intuitions are a nice guide, but knowing how to turn the crank and churn out the calculations is also crucial for the cases where intuitive thinking doesn't scale.
Re: Sets and Probability
#5The set-based intuitions are a nice guide, but knowing how to turn the crank and churn out the calculations is also crucial for the cases where intuitive thinking doesn't scale.
yeah, I also liked this guide. Would love more articles about probabilities (but i always loved this topic :)), there's only one exception: the "3 door problem" (Monty Hall problem). In my opinion the general misconception about this problem does not stem from a misunderstanding of probabilites but a misconception about the moderator (who plays by his own rules [as a bad actor] - which is often not really discussed although it changes the whole game).
Well, I would read an article about it by this author anyway ;)
Re: Sets and Probability
#6This method only works because the boxes have the same number of balls. To calculate probabilities by counting outcomes you have to start with outcomes that all have equal probabilities.
Re: Sets and Probability
#7The set-based intuitions are a nice guide, but knowing how to turn the crank and churn out the calculations is also crucial for the cases where intuitive thinking doesn't scale.
yeah, I also liked this guide. Would love more articles about probabilities (but i always loved this topic :)), there's only one exception: the "3 door problem" (Monty Hall problem). In my opinion the general misconception about this problem does not stem from a misunderstanding of probabilites but a misconception about the moderator (who plays by his own rules [as a bad actor] - which is often not really discussed a…
Not sure what you mean with "bad actor" - the host/moderator is not an adversary, his rules are fixed from the outset (see e.g. Standard Assuptions in [1])
These rules imply that new information is revealed, and based on the new information it is advantageous to switch.
The trickyness of the Monty Hall Problem lies in identifying that indeed new information has been revealed, which seems counter-intuitive.
Re: Sets and Probability
#8This method only works because the boxes have the same number of balls. To calculate probabilities by counting outcomes you have to start with outcomes that all have equal probabilities.
It's a special-case of a general principle that works regardless of the weighting. Instead of integer counting, do real counting with unity.
Re: Sets and Probability
#9The set-based intuitions are a nice guide, but knowing how to turn the crank and churn out the calculations is also crucial for the cases where intuitive thinking doesn't scale.
It's indeed a nice guide. One place where the intuition stops unexpectedly, is calculating the probability of getting 2 reds balls out (without replacement). In the situation with all balls together, the chance would be 1/4. But with two separate boxes, the probability would change to 4999/20000 (1/2 * (1/100 * (0 + 1/2 * 99/100) + 99/100 * (1/2 * 1/100 + 1/2 * 98/99))).
Re: Sets and Probability
#10Earlier quoted context omitted.
yeah, I also liked this guide. Would love more articles about probabilities (but i always loved this topic :)), there's only one exception: the "3 door problem" (Monty Hall problem). In my opinion the general misconception about this problem does not stem from a misunderstanding of probabilites but a misconception about the moderator (who plays by his own rules [as a bad actor] - which is often not really discussed a…
Not sure what you mean with "bad actor" - the host/moderator is not an adversary, his rules are fixed from the outset (see e.g. Standard Assuptions in [1]) These rules imply that new information is revealed, and based on the new information it is advantageous to switch. The trickyness of the Monty Hall Problem lies in identifying that indeed new information has been revealed, which seems counter-intuitive. [1] https:…
Good on wikipedia for having them, but in my experience those "standard assumptions" are often left out when stating the problem.