Algebra.Com's Answer #828027 by ikleyn(52787)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A group of 15 individuals is used for a biological case study.
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document.write( "The group contains 3 people with blood type O, 5 with blood type A,
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document.write( "4 with blood type B, and 3 with blood type AB.
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document.write( "What is the probability that a random sample of 7 will contain
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document.write( "2 persons with blood type O, 2 persons with blood type A,
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document.write( "2 persons with blood type B, and 1 person with blood type AB?
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document.write( "This problem is solved in two steps.\r\n" );
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document.write( "First step is to compute the number of all possible different groups of 7\r\n" );
document.write( "individuals that can be formed/selected from 15 individuals.\r\n" );
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document.write( "This number is the number of combinations of 15 individuals taken 7 at a time\r\n" );
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document.write( "  =  =  = 6435.\r\n" );
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document.write( "Second step is to compute the number of favorable groups of 7 individuals with given compositions.\r\n" );
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document.write( "Two persons with blood type O can be chosen from 3 people with blood type O by  = 3 different ways.\r\n" );
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document.write( "Two persons with blood type A can be chosen from 5 people with blood type A by  = 10 different ways.\r\n" );
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document.write( "Two persons with blood type B can be chosen from 4 people with blood type B by  = 6 different ways.\r\n" );
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document.write( "One person with blood type AB can be chosen from 3 people with blood type AB by  = 3 different ways.\r\n" );
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document.write( "So, 3*10*6*3 = 540 different groups can be formed of the given composition.\r\n" );
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document.write( "Then the probability under the problem's question is P =  =  =  .\r\n" );
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document.write( "ANSWER. The probability that a random sample of 7 will contain \r\n" );
document.write( " 2 persons with blood type O, 2 persons with blood type A, \r\n" );
document.write( " 2 persons with blood type B, and 1 person with blood type AB is = 0.0839 (rounded).\r\n" );
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document.write( "Solved.\r
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