Challenge · Medium problem

A signal passes from $S$ to $T$ through a network with two parallel paths. The upper path contains two components in series, each functioning independently with probability $\dfrac{9}{10}$. The lower path contains a single component functioning with probability $\dfrac{4}{5}$. The signal gets through if at least one path is fully functional, and all components act independently. The probability the signal gets through is $\dfrac{m}{n}$ in lowest terms. Find $m+n$.