20090205, 17:30  #1 
Aug 2003
Snicker, AL
3BF_{16} Posts 
bowl of nuts
This is not so much of a puzzle as it is a question about probability.
There is a large bowl of mixed nuts in front of you. The nuts are varying sizes and shapes including pecans, cashews, brasil nuts, etc. The smallest nuts in the bowl are peanuts and they comprise 50% of the total. You reach into the bowl with your human size forefinger and thumb and pull out one nut. What is the probability it will be a peanut? Before you make a fast answer, let me warn you that in actual practice, it is NOT 50%. DarJones 
20090205, 17:59  #2  
"Mark"
Apr 2003
Between here and the
2^{3}·809 Posts 
Quote:
All I'm saying is that I highly doubt that the answer is fixed. 

20090205, 18:25  #3 
Aug 2003
Snicker, AL
7×137 Posts 
whether it is near the middle or near the edge that you get a nut should not make a significant difference. Think about the way your thumb and forefinger work and you will see why.
The nuts are truly mixed meaning various sizes and species are spread throughout the bowl. The objective is to pick a single nut out of the bowl without consciously 'selecting' by feel or by sight. Just let whichever one your fingers get be the one you remove. Think about this a while and you will find that it is a very interesting problem. The size of your fingers is the biggest single factor. DarJones Last fiddled with by Fusion_power on 20090205 at 18:25 
20090205, 23:17  #4  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
Quote:
(Yes, I know the Law of Small Numbers, but if you knew the secret ...) There's a way for the ticketdrawer to minimize the effect of this method (and I advise all of you to see that drawings are done this way if you have any influence): Thoroughly, and I mean thoroughly mix the raffle tickets before drawing. Do so in a way that doesn't just shuffle tickets without changing their orientations, but actually flips them, repeatedly, in relation to one another, such that no group of tickets remains together from start to finish. When you see one of those drawings from a big rotating drum that seems to mix the tickets  that may not be good enough. The drum should have interior paddles, as in a clothes dryer, to help flip and scatter the tickets in relation to each other during the rotations, and should be rotated many, many times (not very rapidly, either) between insertion of tickets and the drawing. Last fiddled with by cheesehead on 20090205 at 23:20 

20090206, 00:03  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6302_{10} Posts 
For the nuts, I presume 50% is measured by the number of individual pieces? If so, then peanuts will comprise less then 50% by volume. I think the probability of drawing a peanut will be related to the overall volume ratios in the bowl.
For the raffle tickets, it is well known that folded vs nonfolded tickets changes the odds of being drawn. They mix differently when the bowl of stirred and often drawers will draw from certain locations. Leaving out the exact details in line with cheesehead's post, but I don't see why, it is easy to work out and not really a secret. Last fiddled with by retina on 20090206 at 00:04 
20090206, 00:32  #6 
Aug 2003
Snicker, AL
1110111111_{2} Posts 
The peanuts are 50% by weight. It is a minor quibble given that most mixed nuts are sold by weight. I thought carefully about including this in the original question then decided to let folks make an educated guess. They could be mixed by weight, by volume, or by count. Presume the peanuts weigh exactly 1/2 the total weight of the bowl of nuts.
DarJones 
20090206, 00:34  #7  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10011110010110_{2} Posts 
Quote:
Quote:
If it was by intial volume (10 L of peantus, 10L of others, mixed then poured), then we are talking a better challenge. Also, was the bowl vibrated at all (even subtlely) after the random mixed nuts were placed in it? This would bias away from the goobers. They ain't even really nuts! Last fiddled with by Uncwilly on 20090206 at 00:39 Reason: Fusion's contemporaneous post. 

20090206, 00:43  #8 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2·23·137 Posts 
So also with 50% by weight we still get a volume difference. Some nuts will be more dense by than others. I would guess that peanuts are quite dense so would comprise less than 50% by volume and thus have a lower expectation of begin picked.

20090206, 16:31  #9 
Aug 2003
Snicker, AL
7·137 Posts 
The lleast dense nuts in the mix are pecans. The most dense are brasil nuts. The mixture is random and relatively even throughout the bowl.
The interesting thing I found is that there was an interaction between the size of my fingers and the size of the nut I picked up at random. My fingers tended to pick up larger nuts about 70% of the time. The shape of the nuts played a part since I tended to pick pecans much more often than expected given that they are a very small part of the mix. There must be a mathematical rule that would explain this. DarJones 
20090209, 16:38  #10 
Apr 2008
Regensburg..^~^..Plzeň
5·17 Posts 
Are you sure it doesn't have something to do with Dar Jones likes Pecans? I usually come up with a cashew which I like almost as much as a Brazil nut. So I suppose the shape has a slight effect the brazil nuts tend to slip away if my mother(RIP) hasn't gotten them first. I rarely come up with a peanut.
nelson Last fiddled with by Nelson on 20090209 at 16:40 Reason: don't really care for peanuts that much. 
20120921, 19:42  #11 
Sep 2012
Massachusetts
1 Posts 
randomness in raffle drawings
I am working with non profit charitable organizations on running raffles. They are heavily regulated by state. Most require the use of two part raffle tickets of which one part is placed in a bin and the winner is drawn. I think that in order to have perfetc randomness the drum has to be turned enought imes so that every ticket (let's say there are 1000) has to be in a difefernt place in the drum from whe the drum was first turned. I doubt this owuld ever happen so I question if the traditional way of selecting a raffle ticket is truely random and fair. The only people really making mnoney are the raffle ticket printers. Is there a mor erandom and firer way to have a raffle drawing?

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