# TPCW3: Uh-Oh.

Gwen Stacy and Spiderman are separated on a $$3$$ by $$3$$ grid at lattice points inside $$(0, 0)$$, $$(3, 3)$$, $$(0,3)$$, and $$(3,0)$$. Spiderman is at $$(3, 3)$$, and Gwen is at $$(0, 0)$$. Spiderman must get to Gwen. Unfortunately, Electro is at $$(1,1)$$, and Spiderman can either avoid Electro, or if he gets to Electro, he has a $$\frac{2}{3}$$ chance of passing easily and safely, and $$\frac{1}{9}$$ chance of barely passing, but if this happens, he gets thrown back to $$(2, 2)$$. Gwen cannot move at all, and Spiderman can only move left or down $$1$$ unit at a time (with equal probability).

The probability that Spiderman gets to Gwen is $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime and positive integers. Find $$a+b$$.

×