\(A=\left(1-\frac{1}{12}\right)\left(1-\frac{1}{13}\right)\left(1-\frac{1}{14}\right)...\left(1-\frac{1}{18}\right)\)
\(=\frac{11}{12}.\frac{12}{13}.\frac{13}{14}...\frac{17}{18}\)
\(=\frac{11}{18}\)
\(_{\left(1-\frac{1}{12}\right)\times\left(1-\frac{1}{13}\right)\times\left(1-\frac{1}{14}\right)\times\left(1-\frac{1}{15}\right)\times\left(1-\frac{1}{16}\right)\times\left(1-\frac{1}{17}\right)\times\left(1-\frac{1}{18}\right)}\)
= \(_{\frac{11}{12}\times\frac{12}{13}\times\frac{13}{14}\times\frac{14}{15}\times\frac{15}{16}\times\frac{16}{17}\times\frac{17}{18}}\)
=\(_{\frac{11\times12\times13\times14\times15\times16\times17}{12\times13\times14\times15\times16\times17\times18}}\)
=\(_{\frac{11}{18}}\)