Question

Answer 1

\(M=\left(1-\dfrac{1}{31}\right)\left(1-\dfrac{1}{32}\right)\cdot...\cdot\left(1-\dfrac{1}{2017}\right)\left(1-\dfrac{1}{2018}\right)\)

\(=\dfrac{30}{31}\cdot\dfrac{31}{32}\cdot...\cdot\dfrac{2016}{2017}\cdot\dfrac{2017}{2018}\)

\(=\dfrac{30}{2018}=\dfrac{15}{1009}\)