As in Example 1.3.6, consider telegraph signals dot and dash sent in the proportion 3:4, where erratic

Question:

As in Example 1.3.6, consider telegraph signals "dot" and "dash" sent in the proportion 3:4, where erratic transmissions cause a dot to become a dash with probability 1/4 and a dash to become a dot with probability 1/3.
(a) If a dash is received, what is the probability that a dash has been sent?
(b) Assuming independence between signals, if the message dot-dot was received, what is the probability of the four possible messages that could have been sent?
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