2 ms·
Yes, that's exactly right. Paraphrasing what another poster wrote about this on Twitter: "You would rather go fishing in a lake where you just saw someone else
by eigenvalue 3y ago
Yes, that's exactly right. Paraphrasing what another poster wrote about this on Twitter: "You would rather go fishing in a lake where you just saw someone else catch a fish."
Also, the logic continues as you draw more balls from the urn. If the second ball is ALSO red, then you have even more evidence suggesting that N was selected in such a way as to make red the overwhelmingly more likely choice. Thus the chance of the third ball being red is even higher than the 66% probability in the second draw.
- Terr_ 3y agoTo extend the fishing metaphor, the premise of ~100 balls is also important: If each lake could only sustain one (good) fish, you would actively avoid anywhere someone had already caught one from.
- user_7832 3y agoI guess the counterpoint to this is as the number of balls goes from 100 to infinite, it becomes increasingly harder to predict, correct?
- cornel_io 3y agoNo, the higher the count goes the closer it becomes to the single removed ball not mattering at all, so the only thing that matters is the information you got about which urn you're selecting from.
- eigenvalue 3y agoAccording to the original poster on Twitter: "One cool thing is that this probability doesn’t change if you replace 100 in the statement of the problem with some other number (as long as it’s at least 2), as these arguments show." Source: https://x.com/littmath/status/1752167731682492522?s=46 https://x.com/littmath/status/1752167731682492522?s=46
- pvg 3y agoThat's "what's the probability you've caught the world's meanest fish".
- deleted 3y ago[deleted]