Question 1210441
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Giving a test to a group of students, the grades and gender are summarized below

<pre>
         A   B   C   Total
Male    12  39  17    68
Female  16  11  33    60
Total   28  50  50   128
</pre>If one student is chosen at random,
find the probability that the student was female GIVEN they got a 'A.
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<pre>
This problem is on conditional probability.


I will solve it using the method of reducing the space of event.


Our condition " GIVEN they got a 'A' "  allows me to consider the first column 
named  'A'  as a reduced space of event: so, I am looking for events in column 'A', only.


Thus I have 16 favorable students in this column (females) 
with the total 28 students in column 'A'.


Therefore, the answer is  P = {{{16/28}}} = {{{4/7}}}.
</pre>

At this point, the problem is solved completely with all necessary explanations.