document.write( "Question 1196709: If you have a jar full of 400 marbles, with 4 colors distributed equally, how many marbles must you pick randomly to have > 90% chance of having at least one of each color? \n" ); document.write( "
Algebra.Com's Answer #829714 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "I don't see an easy path to computing the probability, but shown below is some information that may help another tutor figure it out(?)   \r
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document.write( "I did a simulation using C code and used a true random number generator.  
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document.write( "Here are the average number of selections needed to get one of each color for several runs of the simulation.  Each run represents 100000 trials, where a single trial ends when at least one of each color has been selected:\r
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document.write( "1st run:  8.333
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document.write( "2nd run:  8.324
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document.write( "3rd run:  8.341
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document.write( "4th run:  8.337\r
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document.write( "-------\r
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document.write( "Added code to capture the distribution of picks.  Here is a 5th run with the distribution shown (46 is the max number of picks for this run):\r
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document.write( "(Based on this emperical data, it seems 13 picks gives 90% confidence.)\r
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document.write( "Average number of selections: 8.351
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document.write( "Number of selections required, distribution:
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document.write( "0    0
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document.write( "1    0
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document.write( "2    0
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document.write( "3    0
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document.write( "4    9372
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document.write( "5    13912
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document.write( "6    14668
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document.write( "7    13126
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document.write( "8    11144
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document.write( "9    8773
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document.write( "10    6969
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document.write( "11    5327
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document.write( "12    4082
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document.write( "13    3102
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document.write( "14    2412
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document.write( "15    1703
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document.write( "16    1346
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document.write( "17    971
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document.write( "18    747
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document.write( "19    572
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document.write( "20    445
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document.write( "21    311
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document.write( "22    252
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document.write( "23    192
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document.write( "24    151
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document.write( "25    110
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document.write( "26    83
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document.write( "27    62
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document.write( "28    34
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document.write( "29    26
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document.write( "30    27
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document.write( "31    25
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document.write( "32    15
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document.write( "33    11
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document.write( "34    12
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document.write( "35    6
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document.write( "36    1
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document.write( "37    1
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document.write( "38    1
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document.write( "39    2
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document.write( "40    1
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document.write( "41    3
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document.write( "42    0
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document.write( "43    0
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document.write( "44    2
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document.write( "45    0
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document.write( "46    1
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document.write( "47    0
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document.write( "48    0
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document.write( "49    0
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document.write( "50    0
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document.write( "... all zero through index [99] (and none greater than 99 either)\r
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