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 a 0 two thirds of the time. When a 1 is sent, the probability that it is received correctly is 4/5 and the probability that it is received incorrectly (as a 0) is 1/5. When a 0 is sent, the probability that it is received correctly is 3/5 and the probability that it is received incorrectly (as a 1) is 2/5. Use Bayes' theorem to find the probability that a 0 was transmitted, given that a 0 was received.