A placement test is given by a university to predict student success in a calculus course. On average, 70% of students who take the test pass it, and 87% of those who pass the test also pass the course, whereas 8% of those who fail the test pass the course.
(a) What is the probability that a student taking the placement test and the calculus course will pass the course?
(b) If a student passed the course, what is the probability that he or she passed the test?