Marbles in a pouch

rodericj · 2004-01-04, 18:26

Hi,

I just found this forum and I love it! Non stop laughs from beginning to end.

Anyway. I heard this puzzle some time last year and I thought it was fun. I searched for this on this forum and I couldn't find it so I assume nobody posted. The puzzle is like this:

You are given 2 pouches. In each pouch is an equal amount of marbles. One pouch has all red marbles and one pouch has all blue marbles. The idea is to rearrange the number of marbles in each pouch so that a random selection from either pouch will maximize the probability that a blue marble will be selected.

As far as I know there is one solution. PM's are the best way to get me the answer. I think this one should be pretty quick for most of you.

Wacky · 2004-01-06, 00:34

Hey, a great puzzle. I don't know how to handle red and blue. My procedure is only black and white.

Take one marble from the pouch of the black (blue) marbles and set it aside for the moment.
Place all the other marbles (from both pouches) in the same pouch.
Place the single marble in the other pouch.

On a probablistic basis, assuming that the selection is make by choosing a pouch at random and then selecting a marble from that pouch at random, the probability of selecting a blue marble approaches unity as the total number of marbles increases.

Fusion_power · 2004-01-06, 02:31

Your problem description seems to be a bit of a problem. As wacky suggested, anything that changes the ratio of red to blue can impact the probability of picking a blue first.

You could pour some portion of the blue marbles into the red bag.

Fusion

Uncwilly · 2004-01-06, 06:16

Wacky,

I think that you may have slipped a cog.

The likelyhood should approach 75% not 100%

Examples spoiled below:
Example1: 2 marbles in each to start
Pouch A 100% chance of blue, Pouch B 33% chance of blue
Total random chance 66.5%

Example2: 100 marbles each
Pouch A 100%, Pouch B 49.7%
Total 74.85%

Example3: 10000 marbles each
Pouch A 100%, Pouch B 49.9975%
Total 74.99875%

Wacky · 2004-01-06, 12:32

Uncwilly,

You are correct.

My brain is not functioning properly. It must be the "cedar fever" :(

Richard

rodericj · 2004-01-07, 03:13

I thought wacky was correct. I was going for 100% chance in the pouch with only 1 blue marble and slightly less than 50% in the other(Has all of the red marbles and all but 1 of the blue marbles).

That is what I was going for. So yes there is a 75% chance of picking a blue marble.

Did I do something wrong? I thought that was a fun puzzle. Has math, has a bag or two. We can all have a good time.

Uncwilly · 2004-01-07, 14:32

It was Fun.

2004-01-04, 18:26	#1
rodericj Jan 2004 Webster, NY 2 Posts	Marbles in a pouch Hi, I just found this forum and I love it! Non stop laughs from beginning to end. Anyway. I heard this puzzle some time last year and I thought it was fun. I searched for this on this forum and I couldn't find it so I assume nobody posted. The puzzle is like this: You are given 2 pouches. In each pouch is an equal amount of marbles. One pouch has all red marbles and one pouch has all blue marbles. The idea is to rearrange the number of marbles in each pouch so that a random selection from either pouch will maximize the probability that a blue marble will be selected. As far as I know there is one solution. PM's are the best way to get me the answer. I think this one should be pretty quick for most of you.

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2004-01-06, 00:34	#2
Wacky Jun 2003 The Texas Hill Country 3²×11² Posts	Hey, a great puzzle. I don't know how to handle red and blue. My procedure is only black and white. Take one marble from the pouch of the black (blue) marbles and set it aside for the moment. Place all the other marbles (from both pouches) in the same pouch. Place the single marble in the other pouch. On a probablistic basis, assuming that the selection is make by choosing a pouch at random and then selecting a marble from that pouch at random, the probability of selecting a blue marble approaches unity as the total number of marbles increases.

2004-01-06, 02:31	#3
Fusion_power Aug 2003 Snicker, AL 3BF₁₆ Posts	Your problem description seems to be a bit of a problem. As wacky suggested, anything that changes the ratio of red to blue can impact the probability of picking a blue first. You could pour some portion of the blue marbles into the red bag. Fusion

2004-01-06, 06:16	#4
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 263A₁₆ Posts	Wacky, I think that you may have slipped a cog. The likelyhood should approach 75% not 100% Examples spoiled below: Example1: 2 marbles in each to start Pouch A 100% chance of blue, Pouch B 33% chance of blue Total random chance 66.5% Example2: 100 marbles each Pouch A 100%, Pouch B 49.7% Total 74.85% Example3: 10000 marbles each Pouch A 100%, Pouch B 49.9975% Total 74.99875%

2004-01-06, 12:32	#5
Wacky Jun 2003 The Texas Hill Country 441₁₆ Posts	Uncwilly, You are correct. My brain is not functioning properly. It must be the "cedar fever" :( Richard

2004-01-07, 03:13	#6
rodericj Jan 2004 Webster, NY 2 Posts	I thought wacky was correct. I was going for 100% chance in the pouch with only 1 blue marble and slightly less than 50% in the other(Has all of the red marbles and all but 1 of the blue marbles). That is what I was going for. So yes there is a 75% chance of picking a blue marble. Did I do something wrong? I thought that was a fun puzzle. Has math, has a bag or two. We can all have a good time.

2004-01-07, 14:32	#7
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2·3·7·233 Posts	It was Fun.