A system was to select a string uniformly at random from the set {RRRR, RS, STT} and then select a letter uniformly at random from the selected string.
The system is run twice (outputting two letters) 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
Q1. How would you find Pr(A∩C)? A and C would be dependent events, as the occurrence of A affects the likelihood of C.
Q2. Once finding Pr(A∩C), is it possible to find Pr(A∩B∩C)?
Thanks for any input/help.