A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is?

Let Event G = original signal is green
E1 = A receives the signal correct
E2 = B receives the signal correct
E = signal received by B is green
P(signal received by B is green) = P(GE1E2) + P(G'E1'E2) + P(G'E1E2') + P(G'E1'E2') = (4/5 × 3/4 × 3/4) + (4/5 × 1/4 × 1/4) + (1/5 × 3/4 × 1/4) + (1/5 × 1/4 × 3/4)
P(E) = 4680
P(G/E) = (4/5 × 3/4 × 3/4) + (1/5 × 1/4 × 1/4) / 4680 = 2023