At a university, an A counts 5 points, a B 4 points, a C 3 points, a D 2 points, and an F 1 point. A student's GPA on the five classes they are taking is computed as the total sum of points divided by 5. They are certain to get an A in Calculus, a B in Physics, and a C in Literature. They are certain to get at least a C in both Economics and Philosophy. In Economics, they have a $\frac{1}{5}$ chance of getting an A, and a $\frac{2}{5}$ chance of getting a B. In Philosophy, they have a $\frac{1}{3}$ chance of getting an A, and a $\frac{1}{3}$ chance of getting a B, independently of what they get in Economics. What is the probability that the student will get a GPA of at least 3.8?