To play a game, you have a box containing 20 fair four-sided dice, with faces {1,2,3,4}. This bag also contains 15 fair six-sided dice (faces {1,2,3,4,5,6}) and 5 fair twenty-sided dice (faces {1,2,3,4,...,19,20}). Call these 3 classes of die "Four", "Six" and "Twenty" (or F, S, and T, for short). You grab one die at random from the box.
Work the following problems by hand (and LaTeX your solutions) unless otherwise stated (but don't be afraid to simulate to check your result!).

Part A: You roll your die one time. What is the probability of the event 6R6, that you roll a 6? Include at least 4 decimal places in your final answer.

Part B: Suppose you roll a 6. What is the probability that the die you chose from the box is a Six-sided die?

Part C: Are the events 6R6 and S independent?