Length of a line segment A line segment of length 1 is cut into two pieces at a completely random point. What is the probability that the longer piece is at least three times the length of the shorter piece?

Attempt 

Let X be the length of the shorter piece and Y be the length of the longer piece.

X: f(x) = 2, 0 &lt; x &lt; 0.5  or f(x) = 0 otherwise

Y: g(y) = 2, 0.5 &lt; y &lt; 1 or g(y) = 0 otherwise

I think the question is asking for P[Y>= 3 X] but I am getting a negative probability.
If the line was cut at 0.25, then the shorter piece would be 0.25 and the longer piece 0.75, 3 times longer. If the line is cut at a point less than 0.25, the longer piece will be more than 3 times the length of the shorter piece. So I think the answer is $\frac{1}{4}$.

Edit: As rightly pointed out by Badam Baplan, this answer doubles to $\frac{1}{2}$ with symmetry since we can cut the line at a point between 0 and 0.25 or between 0.75 and 1.
You just need to have only one probability function . 

considering 

  y = 3x
  y+x = 1
  3x+x = 1
   x  = 1/4


since the probability of one piece having length less than 1/4 answer is 1/4