$(1-\frac{1}{2})\times(1-\frac{1}{3})\times(1-\frac{1}{4})\times(1-\frac{1}{5})\times(1-\frac{1}{6})\times(1-\frac{1}{7})\times(1-\frac{1}{8})$
$=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}$
$=\frac{1}{8}$