A probability problem by Achal Jain

$\begin{aligned} S & = 2+4+5+6+8+10+12+...+94+95+96+98+100 \\ & = \underbrace{\overbrace{2}^a+4+6+...+\overbrace{100}^l}_{n = 50} + \underbrace{\overbrace{5}^a+15+25+...+\overbrace{95}^l}_{n = 10} \\ & = \frac {100(2+100)}2 + \frac {10(5+95)}2 & \small \color{#3D99F6}{\text{Sum of AP }=\frac {n(a+l)}2} \\ & = 2550 + 500 \\ & = \boxed{3050} \end{aligned}$