Question 1150018
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem is on &nbsp;<U>CONDITIONAL &nbsp;PROBABILITY</U>



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Let me re-formulate the problem, to make it (and its solution) more clear.


    There is a universal set U of 100 students.
    Subset  A consists of 85 students.
    Subset B consists of 45 students.
    Subset (A & B) consists of 5 students    //  here   (A & B) means intersection A and B


(a) Jed is from subset B. what is the probability that Jed belongs to subset A, too ?


     In other words, if you take an arbitrary student from B, what is the probability that he / (or she) 
     does belong to the intersection C = (A & B) ?


         The <U>ANSWER</U> is OBVIOUS: the probability P = {{{5/45}}} = {{{1/9}}}.


     On the language of <U>conditional probability</U>, you are given P(B) = 0.45,  P(A & B) = 0.05, and they ask you about  P(A | B).


     By the definition of the conditional probability,  


            P(A | B) = P(A & B) / P(B) = 0.05/0.45 = {{{0.05/0.45}}} = {{{5/45}}} = {{{1/9}}},  the same answer.




(b)  Having (a) solved by me, try to solve (b)  IN THE SAME WAY <U>on your own</U>.


     It is VERY similar (!)
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