document.write( "Question 467339: In a group of 20 person, 5 are females. If 3 persons are picked out of 20 at random, what is the probability that they all are females? What is the probability of atleast one being female? \n" ); document.write( "
Algebra.Com's Answer #320636 by Edwin McCravy(20060)\"\" \"About 
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document.write( "The other tutor's solution is incorrect.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In a group of 20 person, 5 are females. If 3 persons are picked out of 20 at random, what is the probability that they all are females?
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document.write( " There are C(5,3) ways to pick a group of 3 females out of the 5.\r\n" );
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document.write( "There are C(20,3) ways to pick any group of 3 persons\r\n" );
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document.write( "So the probability is \"C%285%2C3%29%2FC%2820%2C3%29=+10%2F1140+=+1%2F114\"\r\n" );
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\n" ); document.write( "What is the probability of atleast one being female?
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document.write( "We find the probability of the complement event and subtract\r\n" );
document.write( "from 1.\r\n" );
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document.write( "The complement event of at least one female is having no females\r\n" );
document.write( "which means all males.\r\n" );
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document.write( "Since there are 5 females, there are 15 males.\r\n" );
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document.write( "So there are C(15,3) ways to pick a group of 3 males out of the 15.\r\n" );
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document.write( "There are C(20,3) ways to pick any group of 3 persons\r\n" );
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document.write( "So the probability is \"C%2815%2C3%29%2FC%2820%2C3%29=+455%2F1140+=+91%2F228\"\r\n" );
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document.write( "Edwin
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