Predict" the rate for the decay $\tau^{-} \rightarrow \mathrm{e}^{-} \bar{\nu}_e \nu_\tau$, where the $\tau$-lepton has mass $1.8 \mathrm{GeV}$. The observed branching ratio of this decay mode is approximately $20 \%$. Calculate the lifetime of the $\tau$-lepton. Can you explain this branching ratio?