document.write( "Question 1177086: A consumer goods company recruits several graduating students from universities each year. Concerned about the high cost of training new employees, the company instituted a review of attrition among new recruits. Over five years, 30% of new recruits came from a local university, and the balance came from a more distant universities. Of the new recruits, 20% of those who were students from a local university resigned within two years, while 45% of other students resigned. Given that a student resigned within two years, what is the probability that she hired from
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Algebra.Com's Answer #850542 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "A consumer goods company recruits several graduating students from universities each year.
\n" ); document.write( "Concerned about the high cost of training new employees, the company instituted a review
\n" ); document.write( "of attrition among new recruits. Over five years, 30% of new recruits came from a local
\n" ); document.write( "university, and the balance came from a more distant universities. Of the new recruits,
\n" ); document.write( "20% of those who were students from a local university resigned within two years,
\n" ); document.write( "while 45% of other students resigned. Given that a student resigned within two years,
\n" ); document.write( "what is the probability that she hired from
\n" ); document.write( "a) a local university?
\n" ); document.write( "b) a more distant university?
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\n" ); document.write( "\n" ); document.write( " Below is a simple and straightforward solution.\r
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document.write( "Let X be the total number of students under consideration.\r\n" );
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document.write( "Of them, 0.3*X are from local university; 0.7*X are from distant universities.\r\n" );
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document.write( "The number of students from local university, who were resigned, is 0.2*0.3*X.\r\n" );
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document.write( "The number of students from distant universities, who were resigned,  is 0.45*0.7*X.\r\n" );
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document.write( "The total number of students, who were resigned, is  (0.2*0.3*X + 0.45*0.7*X).\r\n" );
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document.write( "Question (a) asks about the ratio 0.2*0.3*X  to this sum  (0.2*0.3*X + 0.45*0.7*X).\r\n" );
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document.write( "So, ANSWER to question (a) is  \r\n" );
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document.write( "    P(A) =  = cancel X and calculate = \r\n" );
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document.write( "         =  = 0.16.\r\n" );
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document.write( "Question (b) asks about the ratio 0.45*0.7*X  to the sum  (0.2*0.3*X + 0.45*0.7*X).\r\n" );
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document.write( "So, ANSWER to question (b) is  \r\n" );
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document.write( "    P(b) =  = cancel X and calculate = \r\n" );
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document.write( "         =  = 0.84.\r\n" );
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document.write( "Notice that the sum  0.16 + 0.84 is equal to 1, or 100%, which confirms our calculations.\r\n" );
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Post-solution notice

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\n" ); document.write( "\n" ); document.write( "Notice that my solution is simpler than what by @CPhill, and it does not refer to other theorems:
\n" ); document.write( "it is STRAIGHTFORWARD.\r
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\n" ); document.write( "\n" ); document.write( "If a student solves the problem by the method, shown in the post by @CPhill, it means and it clearly $\"highlight%28highlight%28shows%29%29\"$
\n" ); document.write( "that the student solves the problem by touch, following and repeating the recipes from others
\n" ); document.write( "like a woodpecker and without his or her own understanding.\r
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\n" ); document.write( "\n" ); document.write( "If a student solves the problem by the method from this my post, it means and it clearly $\"highlight%28highlight%28shows%29%29\"$
\n" ); document.write( "that the student understands everything from scratch to the end, and is able to think on his or her own.\r
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\n" ); document.write( "\n" ); document.write( "Actually, a good level student should write these calculation formulas in one breath,
\n" ); document.write( "based on his or her own common sense. It is a sign and a signal of full understanding,
\n" ); document.write( "it is a sign of achieving a good level, and it is what I want to teach you.\r
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