GATE 2021 CS – Question 64

A sender (S) transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities 0.1 and 0.9 respectively, to a receiver (R). In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u,v\in\{H,L\}$. The edge weights are: H to H = 0.3, H to L = 0.7, L to H = 0.8, L to L = 0.2. If the received signal is $H$, the probability that the transmitted signal was $H$ (rounded to 2 decimal places) is ______.