Probability rules..

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 signal received at station \(B\) is green, then the probability that the original signal was green is \(k\).

Find \(\displaystyle{46k~ \text{mod}~ 37}\)

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