SOLUTION: the result of an examinatio. given to a class on three person A,B,C are :40%failed in paper A ;30 %failed in B;25%failed in paper C .15%failed in paper A and B;12%failed in B and C

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Question 1116679: the result of an examinatio. given to a class on three person A,B,C are :40%failed in paper A ;30 %failed in B;25%failed in paper C .15%failed in paper A and B;12%failed in B and C both;10% failed i. A and C ;and 3%failed in all three A,B and C.whag is the probability of a randomly sl3cted candidates passing in all the three papers?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let me re-tell the problem in this equivalent way: 

    Of 100 students, 40 failed in A;   30 failed in B;   25 failed in C;

                     15 failed in AB;  12 failed in BC;  10 failed in AC;

                      3 failed in ABC.

    How many students passed in all three papers ?


Solution 

The number of those who failed at least in one of A, B and/or C is

    40 + 30 + 25 - 15 - 12 - 10 + 3 = 61.       (*)


The rest, 100-61 = 39 passed all three papers.


So,    of the class students,  or 39%, passed all three articles.

Solved.

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If you want to know why and how the formula (*) works, the read these lessons
    - Counting elements in sub-sets of a given finite set
    - Advanced problems on counting elements in sub-sets of a given finite set
in this site.


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