The probability that a student passes a class is
p(P) = 0.57.
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) = 0.74.
What is the probability that a student studied for the class, given that he or she passed the class
(p(S / P))?
Hint: Use Bayes' theorem. (Round your answer to two decimal places.)
p(S / P) =
P(P | S) = P(P and S) / P(S)
0.74 = P(P and S) / 0.54
P(P and S) = 0.74 * 0.54
= 0.3996
So, Using conditional Bayes' theorem,
P(S | P) = P( p and S ) / P(P)
= 0.3996 / 0.57
= 0.70
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