The probability that Sam goes for a run in the morning before work (event R) is 2/5. If he runs then the probability that he catches the train to work (event T) is 2/5. If he does not run then the probability that he catches the train to work is 1/2. If he does not catch the train, then he catches the bus. (a) (5 points) Draw a trte showing the probabilities governing Sam's morning. (b) (5 points) What is the probability that Sam catches the train? (c) (5 points) You are told that Sam made the train what is the probability that he ran?