Chloé chooses a real number uniformly at random from the interval $[0,100]$. Independently, Laurent chooses a real number uniformly at random from the interval $[0,200]$. What is the probability that Laurent's number is greater than twice Chloé's number?

[asy]
size(120, 220);
fill((0,0)--(0,200)--(100,200)--cycle, lightblue+opacity(0.7));
draw((0,0)--(100,0)--(100,200)--(0,200)--cycle);
draw((0,0)--(100,200), red+2);
label("$0$", (0,0), SW);
label("$100$", (100,0), S);
label("$200$", (0,200), W);
label("C", (100,0), SE);
label("L", (0,200), NW);
label("$L>2C$", (50,100), N);
[/asy]