Bài giải:

$B=\left( 1-\frac{1}{4} \right)\times \left( 1-\frac{1}{9} \right)\times \left( 1-\frac{1}{16} \right)\times \left( 1-\frac{1}{25} \right)\times ...\times \left( 1-\frac{1}{100} \right)$

$=\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times \frac{24}{25}\times ...\times \frac{99}{100}$

$=\frac{1\times 3}{2\times 2}\times \frac{2\times 4}{3\times 3}\times \frac{3\times 5}{4\times 4}\times \frac{4\times 6}{5\times 5}\times ...\times \frac{9\times 11}{10\times 10}$

$=\frac{\left( 2\times 3\times 4\times ...\times 9 \right)\times \left( 3\times 4\times 5\times ...\times 11 \right)}{\left( 2\times 3\times 4\times ...\times 10 \right)\times \left( 2\times 3\times 4\times ...\times 10 \right)}$

$=\frac{1}{10}\times \frac{11}{2}=\frac{11}{20}$