A signal which can be green or red with probability \( \frac{4}{5} ...

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A signal which can be green or red with probability \( \frac{4}{5} \) and \( \frac{1}{5} \) respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is \( \frac{3}{4} \). If the
\( \mathrm{P} \)
W signal received at station B is green, then the probability that the original signal was green is
(A) \( \frac{3}{5} \)
(B) \( \frac{6}{7} \)
(C) \( \frac{20}{23} \)
(D) \( \frac{9}{20} \)
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