SOLUTION: The probability that a student passes a class is p(P) = 0.55. The probability that a student studied for a class is p(S) = 0.51. The probability that a student passes a cla

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Question 1142909: The probability that a student passes a class is
p(P) = 0.55.
The probability that a student studied for a class is
p(S) = 0.51.
The probability that a student passes a class given that he or she studied for the class is
p(P / S) = 0.70.
What is the probability that a student studied for the class, given that he or she passed the c

Found 2 solutions by srimankumar45, ikleyn:
Answer by srimankumar45(2)   (Show Source): You can put this solution on YOUR website!
P(p/S)=P(pUS)/P(S)
0.70=X/0.51
X=0.70×0.51
P(S/p)=P(pUS)/P(p)
=(0.70×0.51)/0.55

Solve it and get your answer
Answer by ikleyn(52848)   (Show Source): You can put this solution on YOUR website!
.

            The solution by @srimankumar45 is partly incorrect and partly unreadable.

            I came to bring a correct solution.

            I will solve the problem in two steps.

            Trace attentively my steps to see the difference with the other tutor' solution. 


(a)  The first step is to find  p(P & S).   ( which is the same as  p(P intersection S) )


         p(P | S) = p(P & S)/p(S)     (by the definition of the conditional probability)


     It gives


         0.70 = p(P & S) /0.51,  

         p(P & S) = 0.70*0.51.




(b)  The second step is to get the answer to the problem' question.


         p(S | P) = p(S & P)/p(P)     (by the definition of the conditional probability)


     Notice that p(S & P) = p(P & S) = 0.70*0.51,  as we found it in (a).


     Therefore,  

         p(S | P) =  = 0.649   (approximately)   ANSWER


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