document.write( "Question 1199377: A large company has an inspection system for the batches of new clutches purchased from vendors. A batch typically contains 37 clutches. In the inspection system a random sample of 19 is selected and all are tested. Suppose that there are 11 faulty clutches in the batch of 37. What is the probability that for a given sample there will be 6 faulty clutches?
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Algebra.Com's Answer #833242 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "A large company has an inspection system for the batches of new clutches purchased
\n" ); document.write( "from vendors. A batch typically contains 37 clutches. In the inspection system
\n" ); document.write( "a random sample of 19 $\"highlight%28clutches%29\"$ is selected and all are tested.
\n" ); document.write( "Suppose that there are 11 faulty clutches in the batch of 37 $\"highlight%28clutches%29\"$ .
\n" ); document.write( "What is the probability that for a given sample there will be $\"highlight%28exactly%29\"$ 6 faulty clutches?
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\n" ); document.write( "\n" ); document.write( " I edited your post to make its meaning absolutely clear and unambigous.\r
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document.write( "The probability in this problem is a ratio, whose denominator is the number of combinations\r\n" );
document.write( "of 37 clutches taken 19 at a time\r\n" );
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document.write( "     = 17672631900.\r\n" );
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document.write( "To calculate this great number, I used standard Excel function COMBIN(N,n).\r\n" );
document.write( "It makes calculations faster than I can blink my eyes.\r\n" );
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document.write( "The numerator is  the number of all possible 19-tuples of clutches, containing 6 of 11 faulty clutches.\r\n" );
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document.write( "These special 19-tuples are of the form (6 of 11 faulty clutches, 19-6=13 of 37-11=26 good clutches), and their number is\r\n" );
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document.write( "     =  = 462*10400600 = 4805077200.\r\n" );
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document.write( "Again, the number of combinations in this formula I calculated using Excel function COMBIN.\r\n" );
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document.write( "Thus the final probability is  P =  = 0.2719  (rounded).    ANSWER\r\n" );
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