A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and 0 two-thirds of the time. But there are errors in the transmission. When a 0 is sent, the probability that it is received correctly is 0.8, and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent, the probability that it is received correctly is 0.9, and the probability that it is received incorrectly (as a 0) is 0.1.

(a) Calculate the probability that a 0 is received.

(b)Use Bayes’ Theorem to find the probability that a 0 was transmitted, given that a 0 was received.