document.write( "Question 477798: If you have 14 bad calculators and 24 good calculators and you pull 4 what is the probability that 1 is bad \n" ); document.write( "

Algebra.Com's Answer #852393 by ikleyn(53339) $\"\"$ $\"About$

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\n" ); document.write( "If you have 14 bad calculators and 24 good calculators and you pull 4,
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @Theo is incorrect.\r
\n" ); document.write( "\n" ); document.write( "        It is because @Theo used the Binomial distribution model in his solution, \r
\n" ); document.write( "\n" ); document.write( "        but this model does not work in this case.\r
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\n" ); document.write( "\n" ); document.write( "        See my correct solution below.\r
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document.write( "We should calculate the total number of all possible different quadruples,\r\n" );
document.write( "the number of all possible different quadruples containing 1 bad and 3 good calculators\r\n" );
document.write( "and relate the second quantity to the first quantity.\r\n" );
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document.write( "The total number of all calculators in the problem is 14+24 = 38.\r\n" );
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document.write( "The total number of all possible quadruples of 38 calculators is the number\r\n" );
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document.write( "of combinations  C(38,4) =  = 73815.\r\n" );
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document.write( "The total number of all possible quadruples containing 1 bad and 3 good calculators \r\n" );
document.write( "is this product\r\n" );
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document.write( "    C(14,1)*C(24,3) = 14*2024 = 28336.\r\n" );
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document.write( "Finally, the probability under the problem's question is\r\n" );
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document.write( "    P =  = 0.3839  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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