Given that:
$P(H_s) = 0.1, P(L_s)=0.9$
From the diagram we get,
$P(H_r\mid H_s) = 0.3, \quad P(L_r\mid H_s) = 0.7,$
$P(H_r\mid L_s) = 0.8, \quad P(L_r\mid L_s) = 0.2$
We have to find: $P(H_s\mid H_r)$
By Bayes theorem,
Probability of sending signal ‘H’ given that signal received is ‘H’,
$P(H_s\mid H_r) = \dfrac{P(H_s \cap H_r)}{P(H_r)}$
$\qquad = \dfrac{P(H_r \mid H_s).P(H_s)}{P(H_r \mid H_s).P(H_s)+ P(H_r \mid L_s).P(L_s)}$
$\qquad = \dfrac{0.3 \times 0.1}{0.3 \times 0.1+ 0.8\times 0.9} = 0.04$