SOLUTION: Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 3 17 16 36 Female 14 15 6 35 Total 17 32 22 71 If one student is chosen at ra

        A    B    C   Total
Male    3   17   16    36
Female 14   15    6    35
Total  17   32   22    71

(A)  The answer is obvious: take the total from the row "Male", which is 36, 

     and relate it to the global total, which is 71

         P = .



(B)  Take the number from the cell, which is intersection of the row "Male" 

     and the column "C".  This number is 16.  Relate it to the global total, which is 71

         P = .



(C)  Take total from the row "Male": it is 36.

     Take a total from the column C: it is 22.

      Add these two values and subtract the number in the intersection the row "Male"
      and column "C", which is 16.

      So, you calculate  36 + 22 - 16 = 42.   <<<---=== We subtract 16 in order for do not count it twice.

      This is the number of people in the category "male or got a C".

      Finally, relate it to the global total 71 

          P = .



(D)  This question is about the conditional probability.


     Since the say "GIVEN they got a C", this means that in calculation this probability
     we can reduce our scope to column C.

     In this column, we take the number from row "Male": this number is 16.

     Finally, we relate this number 16 to the total in column C, which is 22.

     The sough probability is  P =  = .