document.write( "Question 420908: A box of 10 flashbulbs contains 2 defective bulbs. A random sample of 2 is selected and tested. Let x be the random variable associated with the number of defective bulbs in the sample\r
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Algebra.Com's Answer #293981 by Edwin McCravy(20056)\"\" \"About 
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document.write( "The probability of selecting no bad ones is the probability of \r\n" );
document.write( "selecting 2 from the 8 good bulbs, which is C(8,2)/C(10,2) or as\r\n" );
document.write( "some people write it (8C2)/(10C2) = 28/45\r\n" );
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document.write( "The probability of selecting 1 good one and one bad one, is the \r\n" );
document.write( "probability of selecting 1 from the 8 good bulbs, and one from \r\n" );
document.write( "the 2 bad ones, which is [C(8,1)C(2,1)]/C(10,2) or as some people \r\n" );
document.write( "write it (8C1*2C1)/(10C2) = 16/45.\r\n" );
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document.write( "The probability of selecting two bad one, is C(2,2)/C(10,2) or \r\n" );
document.write( "as some people write it (2C2)/(10C2) = 1/45.\r\n" );
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document.write( "The probability distribution function is:\r\n" );
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document.write( "x    p(x)\r\n" );
document.write( "0   28/45\r\n" );
document.write( "1   16/45\r\n" );
document.write( "2    1/45\r\n" );
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document.write( "Notice that the sum of those three probabilities is\r\n" );
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document.write( "28/45 + 16/45 + 1/45 = 45/45 = 1.\r\n" );
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document.write( "The expectation is\r\n" );
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document.write( "E(x) = 0*(28/45) + 1*(16/45) + 2*(1/45) = 28/45 + 16/45 + 2/45 = \r\n" );
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document.write( "46/45 = 1.022222\r\n" );
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document.write( "If we were to reach into the same box and draw out 2 bulbs \r\n" );
document.write( "thousands of times we would expect to average picking out \r\n" );
document.write( "1.02222 bad bulbs.  It doesn't mean that we would ever expect \r\n" );
document.write( "to draw out a fraction of a bulb!  That would be impossible.  \r\n" );
document.write( "We just mean that we would expect to average 1.02222 bulbs \r\n" );
document.write( "if we were to repeat the experiment many times.\r\n" );
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document.write( "Edwin
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