29 Jun 09
1 edit
What I meant was that after each 1 minute period either one bottle would fall or no bottles would fall and the odds would be even.
Hence the quickest time for all to fall would be 10minutes and possibly they may never all fall.
After how many minutes would it be a good bet (ie >50'%'😉 that they have all fallen?
I dont know.
29 Jun 09
Originally posted by wolfgang59I still say that after 19 minutes, there is exactly a 50% chance that all bottles have fallen.
What I meant was that after each 1 minute period either one bottle would fall or no bottles would fall and the odds would be even.
Hence the quickest time for all to fall would be 10minutes and possibly they may never all fall.
After how many minutes would it be a good bet (ie >50'%'😉 that they have all fallen?
I dont know.
29 Jun 09
1 edit
Originally posted by wolfgang59I don't think the problem formulated like that makes much sense (and I think ATY would agree with me here), but abstracting from that in that case forkedknight's solution is mathematically correct.
What I meant was that after each 1 minute period either one bottle would fall or no bottles would fall and the odds would be even.
Hence the quickest time for all to fall would be 10minutes and possibly they may never all fall.
After how many minutes would it be a good bet (ie >50'%'😉 that they have all fallen?
I dont know.
29 Jun 09
1 edit
Originally posted by forkedknightApparently you're correct, but it doesn't make much sense to me to consider it implies it is as likely that no bottle falls when we have 10 bottles on the wall as when there is only 1. Still... The problem is what the problem is, so you're right and I was wrong. 🙂
I thought wolfgang just meant that the bottles had to fall in sequence, with the first bottle in the row having a .5 probability of falling each minute.