Q54

A sender $(\textsf{S})$ 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 $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u,v \in \{H,L\}$. For example, the probability that the received signal is $L$ given the transmitted signal was $H$, is $0.7$.

If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.