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 #327423 by Theo(13342)\"\" \"About 
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probability that a calculator is bad is equal to the number of bad calculators divided by the total number of calculators.
\n" ); document.write( "the probability of getting a bad calculator on any 1 draw from the pile is 14/24.
\n" ); document.write( "p(b) is equal to 14/24
\n" ); document.write( "p(g) is equal to 10/24
\n" ); document.write( "p(b) is defined as the probability of getting a bad calculator.
\n" ); document.write( "p(g) is defined as the probability of getting a good calculator.
\n" ); document.write( "you pull 4 calculators out of the pile of 24.
\n" ); document.write( "the probability of exactly x out of the 4 calculators being bad is given by the following table.
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document.write( "n	p(b)^x	        p(g)^(n-x)	nCx	p(x)\r\n" );
document.write( "0	1	        0.030140818	1	0.030140818\r\n" );
document.write( "1	0.583333333	0.072337963	4	0.16878858\r\n" );
document.write( "2	0.340277778	0.173611111	6	0.354456019\r\n" );
document.write( "3	0.19849537	0.416666667	4	0.330825617\r\n" );
document.write( "4	0.115788966	1	        1	0.115788966\r\n" );
document.write( "sum of all probabilities >>>>>>>>>>>>>>>>>>>>   1\r\n" );
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\n" ); document.write( "sum of all probabilities equals 1 as it should.
\n" ); document.write( "n is the number of bad calculators in each sample.
\n" ); document.write( "p(b)^x is the probability of getting x bad calculators out of 4.
\n" ); document.write( "p(g)^(n-x) is the probability of getting (n-x) good calculators out of 4.
\n" ); document.write( "nCx is the number of ways you can get x bad calculators out of 4.
\n" ); document.write( "here's how the formulas work.
\n" ); document.write( "the probability of getting exactly 1 bad calculator out of the 4 would be given by the formula:
\n" ); document.write( "p(b)^1 * p(g)^3 * nC1
\n" ); document.write( "nC1 is equal to 4! / (1!*3!) which is equal to 4
\n" ); document.write( "the probability of getting exactly 1 bad calculator out of a sample of 4 is therefore equal to:
\n" ); document.write( "(14/24)^1 * (10/24)^3 * 4 which is equal to .16878858
\n" ); document.write( "this agrees with the entry for n = 1 in the table, as it should because the formulas used to generate the table are the same formulas being shown here.
\n" ); document.write( "the probability of getting 4 bad calculators when you draw 4 calculators out of the pile of 24 would be calculated as follows:
\n" ); document.write( "(14/24)^4 * (10/24)^0 * 4C4 which equals:
\n" ); document.write( "(14/24)^4 * (10/24)^0 * 1 which equals .1215788966
\n" ); document.write( "this number agrees with the comparable number in the table for 4 bad calculators out of 4 as it should.
\n" ); document.write( "The answer to your question is:
\n" ); document.write( "The probability of getting exactly 1 bad calculator out of the 4 is equal to .16878858\r
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