document.write( "Question 698617: You buy 1000 foam balls and 3 colors of paint from the craft store. Each time you take a new ball out of the bag, it is randomly painted one of your three colors (red, green, blue). You group every 3 balls together. \r
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Algebra.Com's Answer #430951 by Edwin McCravy(20063) $\"\"$ $\"About$

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a) How many groups would you expect to have all three balls painted the same color?
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document.write( "There will be  groups.\r\n" );
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document.write( "The expected number of three of the same color is np where n= and p is\r\n" );
document.write( "the probability of choosing 3 balls painted the same color.\r\n" );
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document.write( "Actually to find the probability of choosing 3 we would be choosing without\r\n" );
document.write( "replacement.  However, since there are 1000 balls, the probability of choosing \r\n" );
document.write( "without replacement is approximately the same as choosing with replacement. \r\n" );
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document.write( "So the probability of selecting 3 reds is\r\n" );
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document.write( "P[(red 1st) AND (red 2nd) AND (red 3rd) = approximately  = .\r\n" );
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document.write( "and the probabilities of choosing 3 greens and of 3 blues are the same. So the\r\n" );
document.write( "probability of selecting 3 of the same color is  =  = .\r\n" );
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document.write( "So the expected number is  groups times  or about 37.04\r\n" );
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\n" ); document.write( "b) If your blue can was 75% empty and only had enough paint to cover 200 balls, how many groups would you expect to have 3 red balls?
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document.write( "On the average when the first 600 have been painted,  of them,\r\n" );
document.write( "or 200 will be red, 200 will be green and 200 will be blue.\r\n" );
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document.write( "But now we're out of blue paint, so on the average, half the \r\n" );
document.write( "remaining 400, or 200, will be red and the other 200 green.\r\n" );
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document.write( "So on the average we end up with 400 reds, 400 greens, and 200 blues.\r\n" );
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document.write( "The expected number of three reds is np where and n = \r\n" );
document.write( "and p is the probability of selecting 3 reds.\r\n" );
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document.write( "Again since there are 1000 balls, the probability of choosing without \r\n" );
document.write( "replacement is approximately the same as choosing with replacement.\r\n" );
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document.write( "The probability of selecting a red ball is  = \r\n" );
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document.write( "P[(red 1st) AND (red 2nd) AND (red 3rd)] = approximately  = .\r\n" );
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document.write( "So the expected number is  groups times  \r\n" );
document.write( "or about 21.33.\r\n" );
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document.write( "Edwin

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