document.write( "Question 936016: There are 15 plugs in a box, of which six are known to be faulty. Three plugs are taken at random from the box. Work out the probability that
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Algebra.Com's Answer #569431 by Edwin McCravy(20060)\"\" \"About 
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There are 15 plugs in a box, of which six are known to be faulty. Three plugs are taken at random from the box.
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document.write( "There are C(15,3) = 455 combinations of 3 plugs we can select from the 15.\r\n" );
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document.write( "There are C(6,3) = 20 combinations of 3 plugs we can select from the 6 faulty\r\n" );
document.write( "ones.\r\n" );
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document.write( "That's 20 out of 455 or 20/455 or 4/91 or only about 4.4% of the time. \r\n" );
document.write( "Answer: 4/91sts of the time.\r\n" );
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\n" ); document.write( "(B) none of the three plugs is faulty
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document.write( "Since there are 6 faulty plugs, and 20 plugs in all, there are 20-6=14 good\r\n" );
document.write( "plugs.  For none of the 3 to be faulty, all 3 must be good:\r\n" );
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document.write( "There are C(14,3) = 364 combinations of 3 plugs we can select from the 14 good\r\n" );
document.write( "plugs.\r\n" );
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document.write( "That's 364 out of 455 or 364/455 or 4/5 or 80% of the time. \r\n" );
document.write( "Answer: 4/5ths of the time. \r\n" );
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\n" ); document.write( "(C) at least one of the three plugs is faulty.
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document.write( "When we see the words \"at least one\", we find the probability of the complement\r\n" );
document.write( "event, and subtract that from 1.\r\n" );
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document.write( "What is the complement event?  It's when we do not have any faulty ones at all.\r\n" );
document.write( "We have already calculated that in (B).\r\n" );
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document.write( "So we subtract 4/5 from 1:    1-4/5 = 5/5-4/5 = 1/5, or 20% of the time.\r\n" );
document.write( "Answer: 1/5th of the time.\r\n" );
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document.write( "Edwin
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