Bayesian Die Identification

You have two fair dice on the table: a 4-sided die with faces 1-4, and a 6-sided die with faces 1-6. One die is selected uniformly at random (each equally likely), and a single roll produces the result 2. What is the probability that the selected die was the 4-sided die? Think through this using Bayes' theorem and explain why the observation of a 2 shifts your belief away from the 50/50 prior.