Assume that E and F are independent events. If Pr (E) = 0.7 and Pr (F|E) = 0.6, find Pr(F).
The enrollment in a certain course is 10% first-year students, 30% sophomores, 40% juniors, and 20% seniors. Past experience has shown that the likelihood of receiving an A in the course is 0.2 for first-year students, 0.4 for sophomores, 0.3 for juniors, and 0.1 for seniors. Find the probability that a student who receives an A is a sophomore.