SOLUTION: Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 12 39 17 68 Female 16 11 33 60 Total 28 50 50 128 If one student

Question 1210441: Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 39 17 68
Female 16 11 33 60
Total 28 50 50 128
If one student is chosen at random,
Find the probability that the student was female GIVEN they got a 'A.
Answer by ikleyn(52968) (Show Source): You can put this solution on YOUR website!
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Giving a test to a group of students, the grades and gender are summarized below

         A   B   C   Total
Male    12  39  17    68
Female  16  11  33    60
Total   28  50  50   128

If one student is chosen at random,
find the probability that the student was female GIVEN they got a 'A.
~~~~~~~~~~~~~~~~~~~~~~~~~

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 =  = .

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

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