document.write( "Question 568292: Hi. Can you please help me with this question!!! \r
\n" ); document.write( "\n" ); document.write( "Sixty percent of a company's sales representatives have completed training seminars. Of these, 80 percent have had increased sales. Overall 56 percent (whether trained or not) have had increased sales. What's the probability of increased sales given that the representative has not been trained? \n" ); document.write( "

Algebra.Com's Answer #852423 by ikleyn(52906) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Sixty percent of a company's sales representatives have completed training seminars.
\n" ); document.write( "Of these, 80 percent have had increased sales. Overall 56 percent (whether trained or not)
\n" ); document.write( "have had increased sales. What's the probability of increased sales
\n" ); document.write( "given that the representative has not been trained?
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document.write( "     |---------------------|------|------------|-----|\r\n" );
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document.write( "     A                     D      C            E     B\r\n" );
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document.write( "                      Figure.\r\n" );
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document.write( "In Figure, interval AB represents all 100% of sales representatives.\r\n" );
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document.write( "Part AC represents 60% of trained sales representatives.\r\n" );
document.write( "Part BC represent the remaining 40% = 0.4 of sales representatives that were not trained.\r\n" );
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document.write( "Part AD represents 80% of AC, which is 0.8*06 = 0.48 = 48% of all representatives\r\n" );
document.write( "who were trained and increased their sales.\r\n" );
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document.write( "The problem says that overall 56% increased their sales.\r\n" );
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document.write( "It means that 56% - 48% = 8% = 0.8 of all employees increased their sales and they are \r\n" );
document.write( "in the set  BC, that were not trained.  I denoted this set of 8% as EB.\r\n" );
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document.write( "The problem wants you determine the ratio  .\r\n" );
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document.write( "It is   =  =  = 0.2 = 20%.    <<<---===  ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "I wrote and placed here this my short solution to contrast it to the long solution by @Theo.\r
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