[tex]L = \frac{1}{1+\frac{1}{3}}\cdot\frac{1}{1+\frac{1}{4}}\cdot\frac{1}{1+\frac{1}{5}} = \frac{1}{\frac{3}{3}+\frac{1}{3}}\cdot\frac{1}{\frac{4}{4}+\frac{1}{4}}\cdot\frac{1}{\frac{5}{5}+\frac{1}{5}}=\frac{1}{\frac{4}{3}}\cdot\frac{1}{\frac{5}{4}}\cdot\frac{1}{\frac{6}{5}}=\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}=\frac{3}{6} = \frac{1}{2}\\\\P = \frac{1}{2}\\\\L = P[/tex]
