\(\Rightarrow\)P=(1-1/2).(1-1/3).(1-1/4).(1-1/5)....(1-1/2011).(1-1/2012)
\(\Rightarrow\)P=\(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}......\dfrac{2010}{2011}.\dfrac{2011}{2012}\)
\(\Rightarrow\)P=\(\dfrac{1.2.3.4.......2010.2011}{2.3.4.5.......2011.2012}\)
\(\Rightarrow\)P=\(\dfrac{1}{2012}\)