In a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams. Assume a randomly selected student is selected from the class. If the student passed the first exam, what is the probability that they passed the second exam?

Required probability is 0.784 .

Step-by-step explanation:

We are given that in a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams.

Let Probability that the students passed the first exam = P(F) = 0.74

     Probability that the students passed the second exam = P(S) = 0.72

     Probability that the students passed both exams = = 0.58

Now, if the student passed the first exam, probability that he passed the second exam is given by the conditional probability of P(S/F) ;

As we know that conditional probability, P(A/B) =

Similarly, P(S/F) = =  {As is same as }

                          = = 0.784

Therefore, probability that he passed the second exam is 0.784 .