Question 1166838
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                     English translation via Google translator


A school of accounting in the capital operates on three shifts: morning, afternoon, and evening. 
In a group of graduating students, 25% graduated from the day shift, 15% from the afternoon shift, 
and the remaining 60% from the evening shift. 
14% of the morning shift graduates achieved the required grade point average, 8% of the afternoon shift, 
and 22% of the evening shift. 
What is the probability, when selecting a student who graduated by achieving the required grade point average, 
that this student came from the day shift?
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        Notice that in this incoming post the notions  " morning shift "  and  " the day shift "  are used as synonyms

        (without warning,  which is not perfect).



<pre>
This problem is about conditional probability.


In the formula for calculation this conditional probability, the denominator should be the part
of students that achieved the required grade point, over all three shifts.

The numerator should be the part of the students from the day shift that achieved the required grade point.


So, the denominator is  0.25*0.14 + 0.15*0.08 + 0.60*0.22 = 0.179.

    the numerator   is  0.25*0.14 = 0.035.


Therefore, the probability under the problem's question is

    P = {{{(0.025*0.14)/(0.25*0.14 + 0.15*0.08 + 0.60*0.22)}}} = {{{0.035/0.179}}} = 0.1955 (rounded).


<U>ANSWER</U>.  The probability, when selecting a student who graduated by achieving the required grade point average, 
         that this student came from the day shift is 0.1955.
</pre>

Solved.


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When I criticize the writers for their mistakes, &nbsp;it is not because I am so bad and not because I want to demonstrate my superiority.


It is for the authors to fix their mistakes and do not repeat them in the future. &nbsp;(And to say &nbsp;" thanks" &nbsp;to me for my cooperation).