At a local high school, 40% of all students who are enrolled in precalculus finish the semester with an A in the class. Of the students who finish precalculus with an A, 80% go on to receive an A in calculus. Of the students who do not finish precalculus with an A, only 30% of the students go on to receive an A in calculus. What is the probability that a randomly chosen student from this school receives an A in both precalculus and calculus?