We break a stick at a uniformly chosen random location. Find the probability that the shorter piece is less than $frac{1}{5}$-th of the original.

The question is the following:

We break a stick at a uniformly chosen random location. Find the probability that the shorter piece is less than $dfrac15$-th of the original.

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My attempt: $$Pleft(X < dfrac15right) = 1 – Pleft(X ge dfrac15right) = 1 – left(1 – dfrac15right) = dfrac15$$
So my answer is that the probability is $dfrac15$.

However, I checked my answer to see if I was right, and I instead found that the answer is $dfrac25$.

Where did I go wrong?