You decide to create a program which reads the letters a and b then outputs those same letters. Here are the characteristics of the program: A third of the output is b's 90% of the time an 'a' is read, it is outputted correctly. 10% it is not outputted correctly (a 'b' is outputted instead). 80% of the time a 'b' is read, it is outputted correctly. 20% it is not (an 'a' is outputted instead). A) Determine the probability that a is outputted. B) Determine the probability that the program read a letter b, given that the output is b.