Information Channel. One of the three words AAAA, BBBB, and CCCC is transmitted via an information channel. The probabilities of these words being transmitted are 0.3, 0.5, and 0.2, respectively. Each...

Information Channel. One of the three words AAAA, BBBB, and CCCC is transmitted via an information channel. The probabilities of these words being transmitted are 0.3, 0.5, and 0.2, respectively. Each letter is transmitted and received correctly with a probability of 0.6, independently of other letters. Since the channel is not perfect, the transmitted letter can change to one of the other two letters with an equal probability of 0.2. What is the probability that the word AAAA was submitted if the word ABCA is received?