document.write( "Question 1120971: An urn contains 4 green , 5 blue , 2 red and 3 yellow marbles . If four marbles are drawn at random , what is the probability that two are blue and two are red ? \n" ); document.write( "

Algebra.Com's Answer #736731 by Edwin McCravy(20060) $\"\"$ $\"About$

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The numerator of the desired probability is the number of ways\r\n" );
document.write( "to choose two blues and two reds:\r\n" );
document.write( "5 blue marbles choose 2 in 5C2 = (5∙4)/(2∙1) = 20/2 = 10 ways.\r\n" );
document.write( "2 red marbles choose 2 in 2C2 = (2∙1)/(2∙1) = 2/2 = 1 way.\r\n" );
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document.write( "So the number of ways to choose 2 blues and 2 reds is:\r\n" );
document.write( "(5C2)(2C2) = 10∙1 = 10 ways. \r\n" );
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document.write( "So the numerator of the desired probability is 10.\r\n" );
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document.write( "The denominator of the desired probability is the number of ways\r\n" );
document.write( "to choose ANY 4 marbles:\r\n" );
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document.write( "4+5+2+3 = 14 marbles choose 4 = 14C4 = (14∙13∙12∙11)/(4∙3∙2∙1) = 24024/24 = 1001 ways.\r\n" );
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document.write( "So the denominator of the desired probability is 1001.\r\n" );
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document.write( "The desired probability is therefore 10/1001. \r\n" );
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document.write( "Edwin

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