14 In a Biology class 85 of students pass the midterm exam I

14. In a Biology class 85% of students pass the midterm exam. If a student passes the midterm exam, there is a 75% they pass the final. If a student does not pass the midterm exam, there is a 55% chance of passing the final exam. a. [3] What is the probability that a student passes both exams? b. [3] If a student passes the final, what is the probability that they passed the midterm exam?

Solution

the probability that a student passes both exams = 0.85x0.55 = 0.4675

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a student passes the final, the probability that they passed the midterm exam = P(AB)/P(A)

= 0.4675/0.75 =0.6233