An injured ant named “Pipee” has got stuck at point $P(\frac25,\frac35)$ inside a square $ABCD$ of the Cartesian Plane where the coordinates of $A,B,C$ and $D$ are respectively $(0,0),(2,0),(2,2)$ and $(0,2)$. Pipee can only move from left to right. If the line which goes through the point $P$ and another point inside $ABCD$ denoted by $Q$ has the slope not more than $\frac34$, only then Pipee can escape. Rafin wants to save Pipee. If he randomly chooses the point $Q$ inside $ABCD$, the probability that Pipee can get free can be written as $\frac rs$ where $r$ and $s$ are co-primes. $r+s=?$

Geometry Probability

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