\(B=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{200}\right)=\left(\frac{2-1}{2}\right)\left(\frac{3-1}{2}\right)...\left(\frac{200-1}{200}\right).\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}...\cdot\frac{198}{199}\cdot\frac{199}{200}=\frac{1}{200}.\)