document.write( "Question 1113083: A urn contains n black balls and n white balls. Three balls are chosen from the urn at random and without replacement. What is the value of n if the probability is 1/12 that all three balls are white? \n" ); document.write( "
Algebra.Com's Answer #728149 by math_helper(2461)\"\" \"About 
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The probability the first ball picked is white is: P(ball 1 is white) = \"+n%2F%282n%29+=+1%2F2+\"
\n" ); document.write( "The probability the 2nd is also white: P(ball 2 is also white) = \"+%28n-1%29%2F%282n-1%29++\"
\n" ); document.write( "The probability the 3rd is also white: P(ball 3 is also white) = \"+%28n-2%29%2F%282n-2%29++\"\r
\n" ); document.write( "\n" ); document.write( "P(all 3 picks are white) = \"+%281%2F2%29%2A%28%28n-1%29%2F%282n-1%29%2A%28n-2%29%2F%282n-2%29%29+=++%281%2F12%29+\" \r
\n" ); document.write( "\n" ); document.write( "Cross multiplying and then simplifying with all terms moved over to the left:\r
\n" ); document.write( "\n" ); document.write( " \"+%28n%5E2+-+6n+%2B+5%29+=+0+\"
\n" ); document.write( " \"+%28n-5%29%28n-1%29+=+0+\"\r
\n" ); document.write( "\n" ); document.write( "Potential solutions are: 1 and 5 (1 and 5 are solutions to the above equation, but might not be solutions to the problem). \r
\n" ); document.write( "\n" ); document.write( "Discard n=1 because that solution is too small to draw 3 balls.
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\n" ); document.write( "Ans: \"+highlight%28n+=+5%29+\"
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\n" ); document.write( "\n" ); document.write( "Check: (1/2)*(4/9)*(3/8) = (12/144) = 1/12 (ok)
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\n" ); document.write( "Edited to remove extra factor of n, which was a carry over from my paper solution where I didn't reduce n/(2n) to 1/2.
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