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   Color Balls in a bag
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   Author  Topic: Color Balls in a bag  (Read 698 times)
ERIC H. ZENGULUS
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Color Balls in a bag  
« on: Jun 27th, 2004, 10:28am »
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There are N balls in the bag. Each one has a distinct color. You draw one ball randomly from the bag, record its color and put it back. Calculate the probability that after T draws you've seen M distinct colors.
 
(T > 0, M > 0, M <= min(T, N) )
« Last Edit: Jul 19th, 2004, 7:52pm by Icarus » IP Logged
Nigel_Parsons
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Re: NEW: HARD: Color Balls in a bag  
« Reply #1 on: Jun 27th, 2004, 5:28pm »
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A bit difficult this one!
 
It relies on the assumption (not stated) that N>M, also that T  [smiley=eqslantgtr.gif] M
 
Otherwise, it may be worth considering!
 
If either of the above is not the case then the possibility is Zero
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ThudnBlunder
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Re: NEW: HARD: Color Balls in a bag  
« Reply #2 on: Jun 27th, 2004, 7:11pm »
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on Jun 27th, 2004, 5:28pm, Nigel_Parsons wrote:
A bit difficult this one!
 
It relies on the assumption (not stated) that N>M, also that T  [smiley=eqslantgtr.gif] M
 
If either of the above is not the case then the possibility is Zero

No. For example, when N = M = T required probability = N!/NN
 
So now you should be able to finish it off.   Wink
 
« Last Edit: Jun 27th, 2004, 8:25pm by ThudnBlunder » IP Logged

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Re: NEW: HARD: Color Balls in a bag  
« Reply #3 on: Jun 28th, 2004, 12:08am »
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[smiley=blacksquare.gif]
I get for the general case the following: NCM [sum]1 [le] k [le] M(-1)M-k MCk (k/N)T.
 
Compare it to THUD&BLUNDER’s answer for M=T=N case.  
[smiley=blacksquare.gif]
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