Question 1177086
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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
a) a local university?
b) a more distant university?
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        Below is a simple and straightforward solution.



<pre>
Let X be the total number of students under consideration.


Of them, 0.3*X are from local university; 0.7*X are from distant universities.


The number of students from local university, who were resigned, is 0.2*0.3*X.


The number of students from distant universities, who were resigned,  is 0.45*0.7*X.


The total number of students, who were resigned, is  (0.2*0.3*X + 0.45*0.7*X).



Question (a) asks about the ratio 0.2*0.3*X  to this sum  (0.2*0.3*X + 0.45*0.7*X).


So, <U>ANSWER</U> to question (a) is  

    P(A) = {{{(0.2*0.3*X)/(0.2*0.3*x + 0.45*0.7*X)}}} = cancel X and calculate = 

         = {{{(0.2*0.3)/(0.2*0.3 + 0.45*0.7)}}} = 0.16.



Question (b) asks about the ratio 0.45*0.7*X  to the sum  (0.2*0.3*X + 0.45*0.7*X).


So, <U>ANSWER</U> to question (b) is  

    P(b) = {{{(0.45*0.7*X)/(0.2*0.3*x + 0.45*0.7*X)}}} = cancel X and calculate = 

         = {{{(0.45*0.7)/(0.2*0.3 + 0.45*0.7)}}} = 0.84.



Notice that the sum  0.16 + 0.84 is equal to 1, or 100%, which confirms our calculations.
</pre>

Solved.


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<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Post-solution notice</H3>

Notice that my solution is simpler than what by @CPhill, and it does not refer to other theorems:
it is STRAIGHTFORWARD.


If a student solves the problem by the method, shown in the post by @CPhill, it means and it clearly &nbsp;{{{highlight(highlight(shows))}}}
that the student solves the problem by touch, following and repeating the recipes from others 
like a woodpecker and without his or her own understanding.


If a student solves the problem by the method from this my post, it means and it  clearly &nbsp;{{{highlight(highlight(shows))}}}
that the student understands everything from scratch to the end, and is able to think on his or her own.


Actually, a good level student should write these calculation formulas in one breath,
based on his or her own common sense. It is a sign and a signal of full understanding,
it is a sign of achieving a good level, and it is what I want to teach you.