The probability that a student passes a class is pP 056 The

The probability that a student passes a class is p(P) = 0.56. The probability that a student studied for a class is p(S) = 0.54. The probability that a student passes a class given that he or she studied for the class is p(P / S) = 0.71. What is the probability that a student studied for the class, given that he or she passed the class (p(S / P))?

Solution

Given p(P) = 0.56; p(S)= 0.54; p(P|S) = 0.71

p(P|S) = p(S and P) /P(S)

p(S and P) = p(P|S)*P(S) = 0.71*0.54=0.3834

now p(S|P) = p(S and P)/p(P) = 0.3834/0.56 = 0.6846