A computer program operates by first selecting a string uniformly at random from the set {RRRR, RS, STT} and then selecting and outputting a letter uniformly at random from the selected string. (a) Complete the following table with the probabilities of the program producing the given outputs when it is run. output R S T probability ? ? ? The program is run twice and the outputs are recorded. Let A be the event that the first output is R. Let B be the event that the second output is S. Let C be the event that the two outputs are the same letter. (b) Find Pr(C). (c) Find Pr(AB), Pr(AC) and Pr(An BnC). (d) Are A and C independent events? (e) Find Pr(AUC).